It •£ 1 No. FHWA/RD-80/027 H H WA - 80-02 / W STRUCTURAL SYSTEMS FOR ZERO -MAINTENANCE PAVEMENTS Vol. 2. Analysis of Anchored Pavements Using ANSYS August 1980 Final Report DEPARTMENT OF RANSPORTATION JAN 1.4 Mil LIBRARY "%■* * Document is available to the public through the National Technical Information Service, Springfield, Virginia 22161 Prepared for FEDERAL HIGHWAY ADMINISTRATION Offices of Research & Development Structures and Applied Mechanics Division Washington, D.C. 20590 FOREWORD This report provides a set of procedures to evaluate the response of an anchored pavement subjected to static vehicle loads, moisture variation in the subgrade, and/or temperature variation through the surface of the pavement. Basically, these procedures consist of the use of two computer programs known as FEMESH and ANSYS. The FEMESH program divides the analytical model into a set of rectangular elements and the ANSYS program evaluates the stresses, strains, and deflections at each of these elements in each material included in the analytical model. The procedures are versatile and capable of solving geometrically complex structures on a geologically complex earth mass. This report is the second volume of a set of three final reports resulting from a research contract, "New Structural Systems for Zero-Maintenance Pavements," issued to Dames & Moore by the Office of Research and Development of the Federal Highway Administration. The objective of this research study was to identify and assess the potential of new and innovative structural concepts and systems to serve as "Zero-Maintenance" pavements. An interim report, "Unique Concepts and Systems for Zero Maintenance Pavements," FHWA-RD-77-76, provides an updated state-of-the-art and comprehensive review of each of the three major structural components of a pavement system: the subgrade, the base and subbase, and the pavement surface. The other two volumes in this final set are reports FHWA/RD-80/026, Volume 1: Analytical and Experimental Studies of an Anchored Pavement, and FHWA/RD-80/028, Volume 3: Anchored Pavement System Designed for Edens Expressway. Volume 1 was published and distributed previously. Copies of Volumes 2 and 3 are being distributed jointly by a single transmittal memorandum primarily to research and development audiences*^ Charles F. Scheffey 1/ Director, Office of Research Federal Highway Administration NOTICE This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof. The contents of this report reflect the views of the Dames & Moore organization which is responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policy of the Department of Transportation. This report does not constitute a standard, specification, or regulation. The United States Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear herein only because they are considered essential to the object of this document. y .A3 Technical Report Documentation Page 1. Report No. FHWA/RD-80/027 2. Government Accession No. 3. Recipient's Catalog No. 4. Title and Subtitle NEW STRUCTURAL SYSTEMS FOR ZERO-MAINTENANCE PAVEMENTS Volume 2: Analysis of Anchored Pavements Using ANSYS 5. Report Date August 19£0 6. Performing Organization Code 7. Author's) 8. Performing Organization Report No. S.K. Saxena and S.G. Militsopoulos 9. Performing Organization Name and Address Dames & Moore 7101 Wisconsin Avenue Washington, D.C. 20014 and Illinois Institute of Technology Civil Engineering Department Chicago, Illinois 60616 10. Work Unit No. (TRAIS) FCP 35E2-042 11. Contract or Grant No. DOT-FH-11-9114 12. Sponsoring Agency Name and Address Offices of Research and Development Federal Highway Administration U.S. Department of Transportation Washington, D.C. 20590 13. Type of Report and Period Covered Final Report 14. Sponsoring Agency Code 15. Supplementary Notes FHWA Contract Manager: Dr. Floyd J. Stanek (HRS-14) Dames & Moore Project Manager: Dr. Mysore S. Nataraja DEPARTMENT OF TOANSPORTATfON i6. Abstract New Structural Systems for Zero-Maintenance Pavements. The purpos* of this study is to investigate the feasibility of designing and qons^nlctJiRg'^gsit-eFfective "Zero-Maintenance" highways. Volume 2: Analysis of Anchored Pavements Using ANSY which provides a set of procedures to evaluate the respon subjected to vehicle static loads, moisture variation in the subgTa^eT^rntr7^r temper- ature variation through the surface of the pavement. These procedures include two computer programs known as FEMESH and ANSYS. The FEMESH program generates rectangu- lar meshes in either a two or three dimensional coordinate system for any prespecifiec number and spacing of nodes. The ANSYS program evaluates the stresses, strains, and the deflections at all elements in each material included in the analytical model. The program can be used for any number of different materials in any direction. In the analysis of heat transfer, the program provides the distribution of temperature as a function of time at predesignated points. The program is versatile and capable of solving complex geometrical structures supported on a geologically complex earth mass. The behavior of an anchored pavement section is evaluated with sets of computer programmed mechanistic models. The manual was written to minimize reference to other publications. This volume is the second in a series. The others in the series are: Volume 1: Analytical and Experimental Studies of an Anchored Pavement, and Volume 3: Anchored Pavement System Designed for Edens Expressway. Abstracts of these volumes are included on page ii of this volume. . ThissfT^iDprt is ja manual Ulan anchored aavement 17. Key Words Anchored pavement pavement systems FEMESH and ANSYS 18. Distribution Statement No restrictions. This document is avail- able to the public through the National Technical Information Service, Springfield, Virginia 22161. 19. Security Classif. (of this report) Unclassified 20. Security Classif. (of this page) Unclassified 21. No. of Pages 144 22. Price Form DOT F 1700.7 (8-72) Reproduction of completed page authorized Abstracts of Related Documents Volume 1: Analytical and Experimental Studies of an Anchored Pavement : A Candidate Zero-Maintenance Pavement This report documents an investigation of the design feasibility and construction cost-effectiveness of an anchored pavement concept for zero maintenance highways. An analytical model is designed to verify computer program results and to investigate construction methods for a full-scale highway section. The purpose of the analytical study is (1) to present thermal, mechanical, and thermomechanical properties of typical materials in a form easily adaptable to computer programs, and (2) to describe environmental and mechanical properties of a conventional slab and an anchored pavement in both continuous and jointed configurations. The two pavements were subject to heat transfer, thermal stress, and mechanical stress analyses. The anchored pavement offers two distinct advantages over a conventional pavement—deflections are lower and more uniform, and stresses in the soil are lower and distributed more widely by the rigid anchors. Subgrade-related failure is less likely to occur if loads are transmitted deeper within the subgrade. Three-dimensional finite element analysis is considered to be the most efficient technique for examining the significance of environmentally induced stress. The use of the finite element method is anticipated as more advanced analytic techniques are developed. Volume 3: Anchored Pavement System Designed for Edens Expressway This report provides an analysis example of an actual pavement and the cost estimate using the anchored system. The actual pavement is the Edens Expressway in Chicago. The report provides the response of the Edens Expressway subjected to mechanical and environmental loads using the an- chored pavement concept. The mechanical and thermal properties of materi- als that could be encountered in future reconstruction of Edens Expressway are presented in a consistent form for computer programming. These proper- ties are viewed as typical design values during investigation of pavement response. The behavior of the anchored pavement under induced temperature loads and weakening of subgrade (by thawing action) is clearly demon- strated. This report will enable application of the anchored pavement concept by any road with heavy traffic. The example problem provides the input parameters of materials and loads for the analysis, the generation of finite element mesh, and the results of the analysis. The computer program ANSYS was used for this study (the manual for the use of the program is presented in Vol. 2 of this series of reports). TABLE OF CONTENTS CHAPTER 1 INTRODUCTION 1 1 . 1 OBJECTIVE -. 1 1 .2 SCOPE 1 l'.2 RELATED 'DOCUMENTS* .................... i CHAPTER 2 ANALYSIS PROCEDURE 3 2.1 COMPUTER CODES USED 3 2.2 PREPARATION OF COMPUTER INPUT 3 2.2.1 System Control Cards 3 2.2.2 ANSYS Problem '. . 5 2.2.3 Login-Logout Procedures for 3atch Users 5 2.2.4 Remote Batch Terminal Commands 7 2.3 ANALYSIS METHODS ; 3 2.3.1 Static Analysis 3 2.3.2 Heat Transfer 10 2.4 LOAD CHARACTERISTICS 1Q 2.5 MATERIAL CHARACTERIZATION 11 CHAPTER 3 OPERATING INSTRUCTIONS FOR FEMESH . . . 22 3.1 FEMESH SOURCE CODE 22 3.2 INPUT DATA 22 3.3 MESH GENERATION EXAMPLE 30 CHAPTER 4 OPERATING INSTRUCTIONS FOR ANSYS 36 4.1 WAVE FRONT SOLUTION AND LIMITATIONS 36 4.2 DATA INPUT INSTRUCTIONS 37 4.2.1 ANSYS Input Data for Static Analysis 38 4.2.2 ANSYS Input Data for Heat Transfer Analysis .... 51 4.2.3 ANSYS Input Oata for Thermal Stress Analysis ... 57 CHAPTER 5 ELEMENT LI3RARY OF ANSYS '. 60 5.1 ELEMENT SELECTION 60 5.2 ELEMENT LIBRARY FOR STATIC ANALYSIS 60 5.2.1 Three-dimensional Isoparametric Solid Element ... 60 5.2.2 Three-dimensional Interface Element 62 m Page 5.3 ELEMENT LIBRARY FOR HEAT TRANSFER- 64 5.3.1 Isoparametric Quadri lateral Temperature Element. . 64 5.3.2 Two-dimensional Conducting Bar 6° 5.4 ELEMENT LIBRARY FOR THERMAL STRESS ANALYSIS 67 5.4.1 Two-dimensional Isoparametric Element 57 5.4.2 Two-dimensional Interface Element 68 CHAPTER 5 CONCLUSION 94 REFERENCES 95 APPENDICES 97 A. NOTATION 97 8. ANALYSIS PROCEDURES 98 C. ELEMENT LIBRARY 107 D. COMPUTER DEFINITIONS AND -COMMUNICATION LINKS .... 130 TV LIST OF TABLES TABLE Page 2.1 EQUILIBRIUM EQUATIONS CStatic Analysis) FOR AN ELEMENT .,.,.,,..,, 12 2.2 EQUILIBRIUM EQUATIONS (.Thermal Analysis) FOR AN ELEMENT . . . , . , . 13 2.3 .MATERIAL PROPERTY NAMES 14 2.4 .MATERIAL PROPERTIES VERSUS ELEMENT SUBROUTINE 15 4.1 ELEMENT REORDERING INSTRUCTIONS ..... 57 4.2 ELEMENT REORDERING FOR SAMPLE PROBLEM 58 5.1 ELEMENT SUMMARY TABLE 71 5.2 INPUT OF ELEMENT PARAiMETERS ON ANSYS PROGRAM DATA CARDS. 73 5.3 UNITS OF INPUT AND OUTPUT PARAMETERS 74 5.4 ISOPARAMETRIC SOLID ELEMENT - THREE-DIMENSIONAL 75 5.5 ISOPARAMETRIC SOLID ELEMENT - THREE-DIMENSIONAL ELEMENT PRINTOUT EXPLANATIONS 77 5.6 INTERFACE ELEMENT - THREE-DIMENSIONAL 79 5.7 INTERFACE ELEMENT - THREE-DIMENSIONAL ELEMENT PRINTOUT EXPLANATIONS 80 5.8 ISOPARAMETRIC QUADRILATERAL TEMPERATURE ELEMENT 81 5.9 ISOPARAMETRIC QUADRILATERAL TEMPERATURE ELEMENT - ELEMENT PRINTOUT EXPLANATIONS 81 5.10 CONDUCTING BAR - TWO-DIMENSIONAL 82 5.11 TWO-DIMENSIONAL ISOPARAMETRIC ELEMENT 83 5.12 TOO-DIMENSIONAL ISOPARAMETRIC ELEMENT, ELEMENT PRINTOUT EXPLANATIONS . . . . . 85 5.13 INTERFACE ELEMENT - TOO-DIMENSIONAL 86 5.14 INTERFACE ELEMENT - TOO- DIMENSIONAL ELEMENT PRINTOUT EXPLANATIONS 87 LIST OF FIGURES FIGURE Page 1 .Soil -Structure Interface Connection 2 2.1 Arbitrary Rectangular Mesh Generation 16 2.2 ANSYS Setup Deck, for CDC Computer 17 2.3 Cufaer 176 Configuration . . . 13 2.4 Summary of ANSYS Analysis Types 19 2.5 Static Load Model (Dimensions and Load Will Vary With Vehicle) 20 2.5 Temperature Load Model 21 3.1 Example of Mesh Generation 31 4.1 ELxample of Element Reordering to Minimize the Wave Front 59 5.1 Three-Dimensional Isoparametric Solid Element .... 88 5.2 Three-Dimensional Isoparametric Solid Element Output. 88 5.3 Three-Dimensional Intarfaca Element 39 5.4 Three- Dimensional Intarfaca Element Output 89 5.5 Isoparametric Quadrilateral Temperature Element ... 90 5.6 Two-Dimensional Conducting Bar Element 91 5.7 Two-Dimensional Isoparametric Element . . 92 5.8 Two-Dimensional Isoparametric Element Output 92 5.9 Two-Dimensional Interface Element 53 5.10 Two-Dimensional Interface Element Output 93 VI CHAPTER 1 INTRODUCTION i . 1 OBJECTIVE The objective of this manual Is to provide the pavement analyst with a ready reference of procedures to obtain the response of an anchored pavement subject to vehicle static loads, moisture variation of the subgrade, and temperature variation at the surface of the pave- ment. 1.2 SCOPE The analysis procedures presented include two computer program packages known as FEMESH and ANSYS. An anchored pavement section of known geometry is chosen, and its behavior is evaluated by sets of mechanistic models which have been computer programed. A subbase and a subgrade material system of known properties are also evaluated. Figure 1.1 shows an interface connection between a finite pavement element and a finite soil element. Those interface elements transmit compression forces, but they don't take any tension forces (that is, disconnect in tension). The manual is composed of six chapters and three appendices. 1 . INTRODUCTION 2. ANALYSIS PROCEDURE 3. OPERATING INSTRUCTIONS FOR FEMESH 4. OPERATING INSTRUCTIONS FOR ANSYS 5. ELEMENT LIBRARY FOR ANSYS 6. CONCLUSION APPENDIX A - NOTATIONS APPENDIX B - THEORETICAL BACKGROUND FOR ANALYSIS METHODS APPENDIX C - THEORETICAL BACKGROUND FOR ELEMENT LIBRARY Each chapter has been organized to provide the user a procedure in order to collect the necessary data and run the program ANSYS. Chapter 2 and 3 describe the necessary steps for computer familiarization and data collection. Chapter 4, the user's guide for ANSYS, has been written so that it can be used independently by the computer analyst. Chapter 5 outlines the elements recommended to be used in ANSYS. 1.3 RELATED DOCUMENTS The manual is developed with the intent of minimizing the amount of reference to other materials. However, references 7 and 8 should be consulted if pre-processing or post-processing routines are desired. interface element f = NODE OF ELEMENT a) Two-dimensional Elements interface element • = NODE OF ELEMENT b) Three-dimensional Elements Figure 1.1 Soil -Structure Interface Connection CHAPTER 2 ANALYSIS PROCEDURE 2.1 COMPUTER CODES USED The software used to conduct the analytical investigation in- cluded two programs - one for mesh generation (elements and nodes) with the name FEMESH and one for the actual analysis called ANSYS. The former was written as a general mesh generator with several criteria in mind: ease of use, minimization of input data required, and ability to generate any two or three dimensional rectangular mesh of arbitrary number and spacing of nodes in the x, y, and z directions (Fig. 2.1). Format for the output of nodal coordinates and element data is consistent with either ANSYS (Engineering ANalysis SYS t ern developed by Swanson) or SAP4 (Structural Analysis Program developed at Berkeley). ANSYS is a proprietary general used, large scale, finite element code with great versatility. Static, heat transfer (steady state and transient), dynamic (modal, forced vibration), electrical, and non- linear (geometric, elastoplastic material, creep) analyses are possible using a large scale element library (a variety of more than 60 elements) comprised of two and three dimensional elements. 2.2 PREPARATION OF COMPUTER INPUT The computer input consists of the system control cards and the ANSYS data deck as shown in Fig. 2.2. The Cyber 176 System shown in Fig. 2.3 was used' in connection with the work at I. LI. 2.2.1 System Control Cards The first card of an input file is interpreted as a NOSBE jobcard and must be of the following format: XXXXX, PARAMETER STRING. CHARGE, USERNAME COMMENTS Where XXXXX Job name, must begin with a letter. Other characters may be alphanumeric. Names longer than 5 characters will be truncated to 5. Jobs submitted through INTERCOM have only the first 3 characters preserved. All of the following parameters are optional, and have default values if not specified. Parameters may be in any order and are separated by commas. TU N is a decimal value for CP Time Limit in seconds. Default is 10. CMFL Ft is the maximum field length in octal words required by the job. It is recommended that if the default Fl is sufficient to process all steps within a job, the CMFL parameter be omitted from the joo card. See -SYSTEM DEFAULT VALUES AND LIMITS- for the default CMFL allocated to each job. ECFL FL is the maximum large core field length in octal TK word blocks required by the job. PJ J_ is the requested priority value and ranges from 1 to 5, Default is 4, MTN N. is the number of 7 track tape drives reserved by the job. PEL or L is the number of 9 track 1600BPI tape drives NTL that will be required by the job. HDL L is the number of 9 track 8Q0BPI tape drives that will be required by the job. GEL L is the number of 9 track 6250BPI tape drives that will be required by the job. DYYMM YY is the dependency string identifier and MM is the dependency count. The charge number is a "six digit (leading zeros must be present) account number, OPTIONALLY followed by a 1 to 3 character suffix for extended accounting . The extended accounting is used for sort- ing when the Billing detail of run is provided monthly. The user- name is given as a "Last Name, Initials." The initials are one or two of your choice as specified at account initialization and entered into the System Access Authorization Table. Any difference between the jobcard entry and the table entry will cause the job to abort. Note that blanks are suppressed when scanning the jobcard, so if only one initial is used, it must be followed by a comma if subse- quent comments are placed on the jobcard. If it is not, the first character of the comment will be picked up as a second initial, and job abort will occur. EXAMPLES RUNID,T10,P4.264786ABC,MILT0N,JE. Test Run RUNID,T10,P4. 264786, MILTON, JE. Comment - No Extended Accounting RUNID,n0,P4.264786,MILT0N,J, If previously set up with one initial The rest of the control cards to call the 2nd revision of ANSYS are as follows: ATTACH(TAPE22,R2ANSYS) C0PYBR(TAPE22,ANSF7) C0PYBR( INPUT, DATA) ANSET(DATA) FILE,TAPEn,8T=C,RT=w",MBL=5120,F0=Sq,SPR=YES,USE. RFl(XXXXXX) (XXXXXX MUST 3E AT LEAST 170000' OCTAL WDS) LDSET(PRESET=ZERO,.MAP=S/ANSMAP ,STAT=TAPE1 1 ) SATISFY, BAMLIB. TAPE20(DATA) 7/8/9 (ANSYS DATA) 7/8/9 6/7/8/9 For big jobs, including three-dimensional elements, it is advised that the 3rd revision/extended core version of ANSYS is used. The control cards for the above revision of ANSYS are as follows: JOBCD, — ,ECXXX. (XXX- NUMBER OF 1000 OCTAL WD ECS BLOCKS REQD) ATTACH, A, R3ANSYSECS. LIBRARY A. RFl(XXXXXX) (XXXXXX MUST BE AT LEAST 170000 OCTAL WDS) FILE, TAPE! 1 ,BT=C,RT=W,MBL=5120,F0=SQ,SPR=YES, USE. ANSYS. 7/8/9 (ANSYS DATA) 7/8/9 6/7/8/9 2.2.2 ANSYS Problem ANSYS input data is set up in a relatively simple fashion that makes learning the code quick and easy. Sequential sets of cards are lettered "A" through "S", "A" being the title card, "S" being a ter- minator. For example, a previous run of FEMESH to generate nodes and elements would supply "F" and "E" cards, respectively. The general purpose of each card group when applied to heat transfer or stress analysis is as follows: A - Title B - Accounting and core aize C - Analysis options (control) D - Element data (types, miscellaneous properties) E - Elements F - Modes H - Material properties L - Load control M - Load control N - Specified displacements (specified temperatures for thermal analysis) - Specified forces (specified heat flow rate for thermal analysis) P - Specified pressures (specified convection for thermal analysis) Q - Temperatures (heat generation rate for thermal analysis) S - Terminator 2.2.3 Loqin-Loaout Procsdures for Batch Users Every BATCH user has a USERNAME and PASSWORD which allows access to the CYBER 176 computer facility. BATCH USERS 1. Dial access Number for desired baud rate: 2. When connection is established, set data phone to "DATA" and then replace hand set. 3. System will respond with: ITEL CONTROL DATA INTERCOM 4. DATE MM/DO/YY TIME HH. MM. SS PLEASE LOGIN 4. You type and send: LOGIN, USERNAME, PASSWORD 5. System will respond with: Date LOGGED IN AT Time WITH USED ID EQUIP/PORT 6. Hit Carriage Return (CR) and system will respond with: LOGIN CREATED Date TODAY IS Date IMPORTANT SYSTEM INFORMATION MESSAGE.... COMMAND- 7. You are now ready to send and receive BATCH commands and messages. In particular, you can now read in card decks and print output from previously run jobs. 8. To submit a 3ATCH job to the system, place the card deck In the reader, mal'e the reader ready, and" type "R" . The deck will then be read into the system. a. mi uer cne iait wra or zne dec.< nas oeen successfully read, the system will once again respond with: COMMAND- TO. When a job is ready for printing, ready the printer and type "ON, LP" . ATI jobs waiting in the output queue will then print until the queue is empty. The terminal will then return to COMMAND mode. 11. To disconnect the terminal from the system, type and send: LOGOUT 12. Restore dataset to "TALK" position; lift phone to check for dial tone and then replace handset. NOTE : This ensures that the phone is properly disconnected. NOTE : The SUP parameter is optional and can be used on the LOGIN command (Step 4): LOGIN .USERNAME, PASSWORD, SUP. The use of the S]1P parameter would result in the elimination of Step 5. 2.2.4 Remote B s tch Terminal Commands All BATCH terminal commands are documented in the INTERCOM V.4 Reference manua* . COMMAND H.I H,E H,0 FILES WAIT, LP GO, LP C R EVICT, - DESCRIPTION Displays your jobs in CYBER 176 input queue Displays your jobs in CYBER 176 execution queue Displays your jobs in Cyber 176 output queue Displays all jobs at your jobsite and the queue they are currently in Suspends job currently printing Continues a suspended print job Resumes interrupted operation Read cards (Last 2 letters of job name) Drop job from input/ output queue before printing E,LP ON, LP RFW BSP,LP,N RTN,,P M,msg REP,,N PRIOR, — , STATUS, — STATUS,,— Kills job while printing Turns line printer logically ON Rewinds current output file Backspace N of output file sectors Halts printing and returns job to output queue with priority P Send message to central site Job is reprinted N additional times (Last 2 characters of output file and then priority you want to raise it to). Status of job (from your site-ID) whose 1st 3 jobname characters are — . Status of all jobs from site- ID--. 2.3 ANALYSIS METHODS This section is intended to give a brief summary of the methods used in the various types of analysis. It is not intended to be a complete theoretical manual or to answer all questions which may arise on the theory behind the ANSYS program. Such detail would expand the already voluminous User's Manual and is better included in a Theoretical Manual. Theoretical details may be obtained by contacting Swanson Analysis Systems, Inc. Figure 2.4 gives a summary of the ANSYS Analy sis types available and may be used as a guide in selecting which type to use. 2.3.1 Static Analysis ■ In the matrix displacement method of analysis based upon finite element idealization, the structure being analyzed must be approximated as an assembly of discrete structural elements connected at a finite number of points (called nodal points). If the force-displacement relationship for each of these discrete structural elements is known (the element "stiffness matrix") then the force-displacement relation- ship for the entire structure can be assembled using standard matrix methods. The general form of the equilibrium equations for each element is: CK.I «,} - {F,} (2J) where, [K ] is the element stiffness matrix {U } is a vector of the element nodal e displacements, and {FA is a vector of the element nodal forces. e For the total structure: [Kl {U} = {F} where, [K] is the total structure stiffness matrix (2.2) X [KJ 1-1 a {11} is a vector of all the nodal displacements in the structure {F} is a vector of all the corresponding nodal forces, thermal forces, and pressure forces 1-1 e If sufficient boundary conditions are specified on (U} to guaran- tee a unique solution, equation 2.2 can be solved to obtain the nodal point displacements at each node in the structure. From these dis- placements the forces and stresses within each structural element can be calculated. For plasticity and creep problems an incremental technique is used. The loading is applied in increments and at each loading level an elastic solution is done, with a correction applied to the next loading step to account for the plasticity and creep occurring during this loading step. In this procedure, the plasticity lags 3 the loading and the calculated stresses are somewhat higher than the true stresses. The amount of this conservative difference can be reduced by increasing the number of load increments or by running iterations with no increase in loading to refine the solution. Unloading and reversed loading can be handled with no difficulty by this technique. The von Mises yield surface is used, along with the Prandtl-Reuss flow relations. The stress-strain curve upon reversed loading is assumed to be the same shape as the vir- gin stress-strain curve, but offset to account for the strain due to previous plastic deformation. Kinematic or isotropic hardening rules are also available for the treatment of cyclic plasticity. The program will handle creep by a similar incremental technique. Both, primary and secondary creep equations are available to the user. The user has the option of selecting either a creep formulation which assumes the stresses decay due to the creep (as in thermal stresses), or a formulation in which the stresses are independent of creep (as in primary stresses). The ANSYS program also includes irradiation induced swelling and creep for use in the analysis of nuclear reactor internals. The swell- ing is not stress dependent and is treated in a manner similar to thermal strains, while the irradiation creep is a stress and temperature dependent pheonomenon and requires an iterative solution. For large deflection analysis the geometry is modified at the end of each load increment so that the total loading is applied to the deformed structure at the next load increment. This procedure thus follows the large deflection load-deflection curve. If the load is applied to the structure in a single step and the rate of convergence to the large deflection is observed, an estimate of the stability of the structure can be made. In particular, if the deflection diverges, the load is above the critical buckling load. This large deflection analysis then becomes a stability check. The basic equations for the formation of the element equilibrium equations are summarized in Table 2.1. The same definitions used here apply to all other analysis types except the heat transfer analysis. 2.3.2 Heat Transfer Transient and steady state heat transfer problems can be solved by finite element techniques analogous to those used for structural analyses. In this case the basic equilibrium equation is: [TUT} + [K]{T} = {Q} (2.3) where, [K] is the thermal conductivity matrix {Q} is the heat flow vector {T} is the vector of the nodal point temperatures [Cl is the specific heat matrix This aquation is identical to the nonlinear dynamic equation except that the mass term does not exist. The solution technique is the same as for the dynamic analysis except that linear and quadratic options are available for this approximation function. This equation is solved in ANSYS at each time point in the heat transfer transient. Material properties (and convection coefficients) can be a function of temperature. In a steady-state analysis the pro- perties are evaluated at the temperature of the previous iteration. In a transient analysis the properties are evaluated at a temperature extrapolated from the previously calculated temperatures. The temperature output from the ANSYS heat transfer analysis is in the required form for input to the ANSYS stress analysis, giving an integrated analysis capability. The basic equations for the formation of the element equilibrium equations are given in Table 2.2. 2.4 LOAD CHARACTERISTICS Pavements are subject to axle weight distributions produced by the traffic volume. Vehicle speed and load duration are not included 10 in this report. The load input consists only of the static weight of an automobile, and the corresponding pavement response is evaluated. Static load can be input as nodal forces (See Fig. 2.5) or element surface pressures. Environmental loads, however, cause more damage to the pavement. Moisture variation is handled by varying the modulus of elasticity of the top four feet of the subgrade soil (of course the variation of modulus with moisture content must be known as an input) . Temperature variation in a time domain can be input in a heat transfer model as shown in Fig. 2.6. The resulting temperature dis- tribution can be handled as a thermal load for a static analysis. 2.5 MATERIAL CHARACTERIZATION All material properties are listed in Table 2.3. Table 2 A represents the material properties needed for the element library used in this report. 11 TABLE 2.1 SQUIL13RIUM...EQUATTGNS (Static Analysis) FOR AN ELEMENT C;< a ]{u 3 > = {? a } - {Q e } + {R a } + (s e > wnara also DO - CT3] T [H] T f [g] T [C][g] dV [H] [TR] e J V {U a } s Nodal displacement vector (in global coordinates) (? a > = Applied nodal load vector {QJ ■ [TRj'CH]' f [gl T [C]{£-.„ > dV = Thermal load vector e j y in {RJ s [TR]'[H]' f [e] T {P} dA = Pressure load vector 6 JA {S } - [fO{AJ s Body force vector e e c {U} = [TR]{U } = [H" 1 ]-Cb> = Nodal displacement vector in local coordinates [TR] s Geometrical transformation matrix [U] s Matrix relating the nodal displacement vector in local coordinates to the displacement function {b} s Vector of the coefficients of the displacement functions {w}. = [e] {b} = Displacement functions [e] = Matrix of displacement shapes Ce} " Cg3"Ch> = elastic strain vector it* } = Thermal strain vector [g] = Matrix relating the elastic strains to the displacement functions [C] = Elastic material property matrix M = [C](U> - ^-[- n H ' stress vector {?} = Distributed load vector [Ml '=-CTR] T [H] T f p [e][e] T dV [H][TR] p = Density (A } - Acceleration vector c 12 TABLE 2.2. EQUILIBRIUM EQUATIONS (Thermal Analysis) rQiR AN ELEMENT CC e ]{7 e } - n< e ]{T a } = {Q e } wnere, CCJ = [H] T /" P CfeKe} 1 dV [H] = Spec" tic neat matrix {T a } = Vector of time derivatives of nodal temperatures [KJ = [H] T f [g] T [!<j[g] dV [H] - [H] T h{e}{e} T dA [H] J V S ■= conductivity matrix (T } = [H~ ]{b^} = Vector of nodal temperatures (Q a ) = [H] 1 J p q{e} dV + [H] 1 7 h (a; dA = Element heat V S flow and heat generation vector .lso, {b.} = Coefficients of temoeture functions z § - = {e} 1 {b*} = Temperature distribution over the element X I L {a} = Vector of temperature distribution shapes p = Density C = Soecific heat P {$ - .} = [g.,.]{b.} = Vector of thermal gradients [3*] = Matrix relating the thermal gradients to the temperature functions [k] = Conductivity material property matrix q = Internal heat generation raze per unit mass T = Coolant temperature c h = Convection coefficient 13 TABLE 2.3 MATERIAL PROPERTY NAMES Property EX EY EZ ALPX ALPY ALPZ NUXY NUYZ NUXZ DENS *C *KXX *KYY *KZZ *HF *VISC Units DescriDtion Force/Area Force/Area Force/Area Strain/Temp Strain /Temp Strain/Temp Mass/Vol Heat/Mass*Oegree Heat * Lenqth Time 3 'Area^Oegree Heat * Lenqth nme : *Area*Oegree Heat * Lenqth Time : *Area*Oegree Heat Time 3 *Area*Oegree Force * Time Length' nu — *•«* GXY Force/Area GYZ Force/Area GXZ Force/Area DAMP *0HMS Resistance*Area Length *EMIS — — . Elastic modulus, X direction Elastic modulus, Y direction Elastic modulus, Z direction Coefficient of thermal expansion, X direction Coefficient of thermal expansion, Y direction Coefficient of thermal expansion, Z direction Poisson's ratio (X strain due to Y stress) Poisson's ratio (Y strain due to z stress) Poisson's ratio (X strain due to Z stress) Mass density Specific heat Thermal conductivity, X direction Thermal conductivity, Y direction Thermal conductivity, Z direction Convection or film coefficient Viscosity Coefficient of friction Shear modulus, X-Y direction Shear modulus, Y-Z direction Shear modulus, X-Z direction K matrix multiplier for damping Electrical resistivity Emissivity * Used only for the Thermal analysis (K20--1) 14 TABLE 2.4 MATERIAL PROPERTIES VERSUS ELEMENT SUBROUTINE Element Subroutine Material Property STIF<12 OR STTF45 EX NUXY ALPX DENS STIF12 OR STIF52 MU STIF55 C /vv <YY DENS STIF32 C KXX DENS 15 y >■ a) Two-dimensional Mesh y — < — b) Three-dimensional Mesh Figure 2.1 Arbitrary Rectangular Mesh Generation 16 ANSYS PROBLEM (A - S) / £. 7-3-9 MULTIPUNCH (COLUMN 1) CARD SYSTEM CONTROL CARDS 5-7-8-9 MULTIPUNCH (COLUMN 1) CARD 7-8-9 MULTIPUNCH CARD (COLUMN 1) hese two cards separate the problem from other cards. Figure 2.2 ANSYS Setup Deck For CDC Computer 17 524 < LCME Sm-NOED MEMORY Figure 2.3 Cuber 176 Configuration 13 TRANSIENT AND STEADY STATE THERMAL ANALYSIS (K20-1)* STATIC ANALYSIS, LINEAR AND NON-LINEAR (K20=0) NON-LINEAR TRANSIENT DYNAMIC ANALYSIS (K20=4) REDUCED LINEAR DYNAMIC TRANSIENT ANALYSIS K20=5) HARMONIC RESPONSE ANALYSIS (K20=3) REDUCED HARMONIC RESPONSE ANALYSIS (K20=6) MODE-FREQUENCY ANALYSIS (K20=2) * ,<20 is the key input on the CI card to select the analysis type. Figure 2.4 Suircnary of ANSYS Analysis Types 19 TJ TJ O U~T7 NLl 1 NL3 Nt2 LD1 NL4 > i ' e a) Truck Model LD2 b) Passenger Auto Model NL - Static Load on Node of Mesh LD = Longitudinal Dimension of Automobile TD = Transverse Dimension of Automobile 1 NL5 -9 NL6 Figure 2.5 Static Load Model (Dimensions and Load Will Vary With Vehicle) 20 UJ TIME STAR" RESTART Figure 2.6 Temperature Load Model (actual values have been explained in the example problem discussed in Volume 3 of this series of reports entitled: Anchored Pave- ment System Designed for Edens Expressway ) 21 CHAPTER 3 OPERATING INSTRUCTIONS FOR FEMESH 3.1 FEMESH SOURCE CODE FEMESH was written with the specific intent of generating rectan- gular meshes for analysis of pavement systems. Provisions for including layers of varying materials is made. Output is available in SAP4 or ANSYS format, either as a punched card or directly written to a tape or mass storage file for use when the analysis is initiated (after data decks ) . 3.2 INPUT DATA The following are the input formats for FEMESH data: Card No. Column Format Variable Description 1 1-30 2QA4 TITLE Job Title 2 1-5 15 NOPT LT.Q generate nodes only 3 6-10 15 N Number of first node (useful when punching different meshes for assembly in ANSYS) 1-5 15 FORM Output format .IE. ANSYS .GT. SAP4 11-15 15 NX No. of nodes in x-di recti on 16-20 15 NY No. of nodes in y-di recti on 21-25 15 NZ No. of nodes in z-direction 26-30 15 NPUNCH .GT. Punched & Printed .IE. Printed only 1-80 1615 MAT Material number 1-80 8F10.0 XP x-coordinates of nodal lines 1-80 8F10.0 YP y-coordinates of nodal lines 1-80 8F1Q.0 1? z-coordi nates of nodal lines Blank card Note: Cards 5, 6, and 7 should be input in increasing order. Use as many 4, 5, 6, and 7 cards as necessary. The listing of the program FEMESH is shown on the following pages (pages 23 through 29). 22 I I I > X LU s. O S- Q- O CD 4-> 00 *l 21 2i2 3- 3 _ ; zi — Cf ""W .1 VU V* — UJ •=" >" u. 2^ « W CI •« 2T. 'j. ZJvi •< C ■J- _J 2li. < — • "< — ! vi < d .5 ; • - -a -j — : - OiS ti 2 -31 3 3 is- — Z — S U. I 2 u: o «J 'j 'JUUU'Jig -o .—• a =»• 2 r 3 -J. -^ ! |-jo- ! U 2 3 i a 52 o ; i 2 -i _ - i>us = ; x - "" a vl _ — ■ ■/ u ' J - : 3 G 2 •< -*. w u) O 2 c >. vj a i ; ■* — -i >■ <j S • U. < -J s o o a = . 2 • >• «e 3 i 2 ^ (J • 2 2 • - 3 — X Si < 2 2 2 - ! U 3 I (J i. 2 2 a O 2 = — 2 UJ vi 13 2 — 2 — 3 ^* ; — x * .2 — x • — — -J '—I 2 •< 3 _l _i 2 2 -T — — i. O 2 X Z 2 •< — «a U 3 IM fl» — 3 — 2 *» -• - 2 x >» "*4 — >- 2 Z Z — • 1 1 1 1 -i — 2 U - J -I ■v. . I 2 IN 2 2 — 2 I ■ 2 a. ij — .rt .-> >. 3 2 — •< < 2 V/l — = 3 _. _i :- — _ '-a .1 vll 2 » 2 « « — 3 — ^J 'o '_ 'J -^ SJ -J U 2 > » 2 > > — •> > 2 » ■> | •> ■> _i > ■> 2 •> > 3 > * 2 > I sJU U UU ■> * -> «•»»•■> > > > > •>' ■> > ^. :- n — %i J" -"» J F* ^z ^j ■j 1M «J .-Vi ."M -•J -m 3 •> ■>» * m .-l r; d <3 >■ 3 C> 2 23 C 4-> C o o oo 13 i- cn o s_ Q- O) cn 4-> IS) IN* -» - 2 »« >» .Nt >- >• 2 2 2 a 2 - - - x -• 1 1 I II I I 2 3 O — •* >• ** 2 U. «S — — — 2 -3 o r -3 <. -3 r* 2 i ii ii — ~5 i -J 1 1 M • 1 i • ~m 1 | 1 2 -* .1 • — ?M ^ >j - (^ • — 3 ; ^ — — a » — — , x — 3 ! • o J a J 3 2 < — — , .J • — * .—• <j* 2 3 2 — * Z • 3 - _l « — • <J — 2 *- »- 3 2 « -1 ■< ■«» C 1 S 3 <"^ 2 -J 2 - <j r 2 a -i 2 2 -*j w — 3 — 2 2 t ■> 2 i* 2 2 2 2 uj ■— 1 -i U* — * -J C 21 2 2 — — — '<*4 J< ^ >4 i. ii i i u vw •*» X >• ^* — vl I * ■-u 2 -J C > •> [ ; ■> ' > f { > | _-i > > ->-» * ■> > > » O a > > ■ 3 _ *NI .% ■> : .%* * > ! > 1 o - a ^ * > ; — ^ 2 • -? > ■ — X ■> > i 2 2, 3< — ■ - > z ■> ; 2 C - — • 2 ■3» 2 > M 2 2 ! ■> — ■> • —* »• 2 • > — > i 2 < -J — •> <■ .y ' 21 : — 2 2 •» 2; > • UJ 2 • 2 > «j ■z- 1 **• 2 , 2 -n 1 •> 2 > | — — ' ■»! 2 - 1 > — ■> j « J - U 2- | •> J > 1 1 -3 2 m .J '-•J ■2- > ! *- *^ | ■— 2 — 2 2 . > — ■> * i. 2: I CI 2 2 J 2 ■> 1 3 ■ji i '— * 2 '_! — ^ > _j > ^ •> 2 -> — 2 ■> — > 1 2 1 2 4» :; ■c 2 > _j > '■ '-*-. < a ~* 3 u *J -> ■> — •> I — i ' 2 -T 2 > • > , C_l l. 1 .-M c\l J L-; LJ > •> i J > > ■J •> ■> -J -• > 9 * * * : J > ? > ■■> > •» > ■vi j r» a s» 2 — "i r* s: -t 2 •— .1 *1 U1 .T ."J 2 J J J J J -3 J J J» 2 — -J J f— .— -1 J- -T J .— 3 T* 3 — >i 24 ! I ■a Z5 C -! -a c o (J 03 S_ O s_ en c » — 2 2 >• •a 3 ; 3 ~5 : ~3 -) i — . 2 — i — a - ■— i 2 3> 2 21 2 21 -I — o - 2:: s z: _ a — — o — 3 — . j — i — . o — — r r r • • 2 2 2 or . . . i • 1 1 1 1 i ■ ^4 - ~i — 2 **■* -•2323 — . — .n n i^l vi u. -3 3 2 2 — <M • 22 >• 2 2 — • It II IE 2 -1 C* ~1 Ui — — — n 2 2 2 -1 2 2 1 1 u ~ J- .1 J p- 3 '__ 2 2 2 2 2 2 vi J 2 — 24 2 S_ i iu 2 — O U3-; j •■d _4 _ - <_) ij -CI (J 3_ vit • O 2 — 2— '2— • ■_* — • ul _J 3 -wJ 2 _) — — — 2: «■* s'j.sa ; <l u — jl — 31 O 2 =: 3 — .j -j _< — -3 3 i > > > 24 ■> X > I— 3 ■> 2 >t -J •>• > ■>• > >l V ■■> •>; -> •>' ■3 r* 2 — ^i 25 -a CD 3 c c o u 2r 3 i. VI I 2 s I ! 3 a — — cvo S V N VI J <t3 i_ CD o 0) — -. (M | >• 2 32 -j VI .1 .1 'J1 - - - — ~ en C ■M CO 5 IN O 21 3 3 o z v> — O 3 r^ 3 — — X X ■< 3 3 O <N i — _ -I — — 'J U U - <vj .-i — . 'j. — 3 X > \ . X » — CM ■•n »3 3 3 3 3 - • x >n -> x ji . - _ HZ— - — — fl XII <1 ui »i ji x '.l »i ii - - »s — o - ..... -.-—— m - *o «— ■ WX>C5<~>» -M X. X — — ' J1 —• -3 a a a — 3. 3 o a a <S <ii ^ <z r r r r 3333333333 —• i">4 "I J ^-» .1 O 3 3 "i •=■ ji 3 ?i 3" n r- ci r> r> 3 "-J 3 ^J J A4 — i — I •> > •> >■■ > 3 — > > > >t ■> 3 > > -x :• r» 3 — "J ■■"> si st -3 .- 3^3 * -* 25 jl I i ' i . li i I i ■> -a 3 O u on I = ra S- cn o i. Q_ sz I -> c I > = - •> — •> — i > x •> : — 3 a ii I li 1 1 Zt — • <>» *-i :r -Jl >3 3 > 4 > . _ ■< < <«•«:■<< ■_! - - - = ^ ■— i 27 c o u I I I I m E <T3 S_ O s_ Q_ O) JZ 4-> en u. I ■» z -> c — • !■*«■> 1 — - 1 » — •> 4-> ■j !•>—:• 00 3 ;•»—•> — » a ■> 1 ■> z * > a > 1 3 -J 3 x 3 -^ .r 3 _s 3 x ^ ivt • 3 > 3 2 , -a j 3 > 3 ■> 3 . u U U 3 * O -> W Wl M I b 1 1 I I I t Ml O -> 3 > J 2 — — — — — — x;-.V4 •> t Ui i_l •— fM ■T .» -fl -d — — — >C> — 3 — — — — — .— -»^.> — 3333333——-" 2 M 2 II i«ii 2 ii « — O _i <J <-! <J —I U _ 2 — I .-vi .-I I O u u y u ■>>•>*-> m * -a ^;^i -; r- =j ^. c — c; coo— a -■ -a .— =; 28 C +-> c o Li. E s_ ai o s_ en c «• ->- _ •> M UJ ■> ■< £ Z — ■> •> - 1 -a] > — 3S — Z > ~ •}* ; Z — •> .u ■> -T Z -?» s » [ — • ! -X •> —i > ! — J •Si _t > i — -C u-I •J- UJ •> o Z MM * ■> — **i ! Z ■>i u -> •< «tl •> l/l > z ^ ! uj ■3" — •> Z — z ■> £ ■> -. .2 XJ — — -> •> a _l I i mm •X "1 ■> 2: n ^* — «M >■ Z * ~ X UJ VI z ■ i in Z a •> vl •> ,3 zz » — — 1 1 c; •> :•■ ■> UJ — a — (VI — s •X 1/1 £1 ■— r z — — 'Z. 3 •> 2 •> Z — ct •< -s :»• vi ■~l ■« v4 — s _« z Z 2 —I — -»l — ■< I II —J 3 <i a z: -j U <J !_l 'J <_i -i J <—> a I*' -3 — <m j -.-.I ,3 .— . a 7> c 29 3.3 MESH GENERATION EXAMPLE To use FEMESH, consider the example shown in Figure 3.1. All that is necessary is to enter the number of nodes in the x, y, and z directions, and the coordinates of the nodal lines in the x, y, and z directions, re- spectively. An example of the input is show below on the FORTRAN coding form. An Example of a FORTRAN Coding Form for FEMESH ISM fanTAAM C*i, M Fun GX23-7327 4U/U050** — FEMESH I 1 . 1 1 | 1-1 -1 1 ■*>■■■■—« S.G.MILI7S0P0UL0S 1-04/04/79 ! ™ 1 — i 1 I ii>d<ii<ijo «••->•• J — r I 'Omi«i WaUm*m1 s=a MEjSH i G rrt .ld 1 1 FN£RAm 1 ON m 1 1 ^2 GO. eco 1 1 i '4 i I i S TOT fTEST i ilPH INnTC I I Ml I 200' "S CO" i mt nrn □TTI" PIT I I l MM Tilt J3QCJ. _6co; i i imii 1 1 nr MU 310 I i I ! I i i M LLMi I I ML I I I ! I I ill I I I I I I ! ! I I i I II I ! I ! i I rm ! ! TT Mill ! ! ! I i i M ! i I I TTT i n ! 1 1 1 I I 1 1 1 1 i i III I I ill I I I I I I I I i ~rn MM I I I i — r l i TT TTI' jrrr TTT 1 1 ! ; i i i ■ i i I TH" 1TTT i I LlA Mil ! I I i ! I I i I I I I I -T "H-r IMT 1 : TT TT~|_i lift i ! I im TT ! r; 1 1 Mil! ! : i m ! ! i ! mi 30 . Q 100. 50. 0. C_) = Node Number / \ = Element Number Hll\ 72 NODES *£«/ 30 ELEMENTS The uncircled numbers indicate the dimensions of the mesh in inches. Figure 3.1 Example of Mesh. Generation 31 "he output of the example proolam using FHflESfl is as follows Output of Example Problem Using FEMESH 3—3 M £ S H GENERATION T £ S T ( ? S I N T £ Q N L Y NOP LT G NC0E5 ONLY Fjfii'U -1 G£ Q SiP<+ L T Q a ^ S Y S NUMSES CF NOOES 1Z MY NZ « A T iLSJAL v -' u H c - £ 3 Q " <- - y £ 5 S ( go I T.C m t o to ?) 1112 3 ,..C £0 >,g .aaa i a a . a a a .ggo ■Z-. CO a a □ 1CG.GCG 2GG.GGQ 5GG.QGG 31G.GGC 32G.CQG .GGG 2CG.GGG 4CG.GGG 6GC.GCG 32 Output of Example Problem Using FEMESH NOOE generation results 1 nnnp .nnnn p n n p 2 .CGGO I G U . G C G G .QGGC 3 n n n n 7 p p . r, n n n . c a, n n 4 ► GGGG iGG. GGGG .GGGG * .nnn p 7 i p . n r. n n . -nnn 6 ,ccaa 32G.aCGG .GGGG 7 - r . r p r, n . q p p n . p P p p 5 5G .GGGG 1GC.GGGG • GGGG Q 5 G . n G G 2PC.QGG0 • GGGG 1G SC .GGQG 3 Q G . G C C G .GGOG i i 5 G . n n n n 71 n. anna .nnnn 12 5C .GGGG 32G.GGGG .GGQG i ? i nn .rrqn . nc^ n ,nn^n 14 1GG .GOOG iac .acac .coaa 1 5 i no .nnnn ? p p .nnnn .nnnn 16 ica ►GGGG' 3GG.G0G0 .GGGG 1 7 i nn . nrinn "in.nnnn . n a a a IS iaa .GGGG 32G.GGGQ .GGGG 1 o . rinnn .nrnr ? n p . p. p p n 2G .GGOG 1CG.GCCG 2GG.GGGG 2 1 . GGGG 2 G G . a C G G • 2GG .GGGG 22 ,GOGC 3GC.GC00 2GC.GGGG 77 .nana 7 1 g . a g a g 2 a a . g a g a 24 .GGGG 32G.GQCG 2aa.GGGC 75 5 f! . n n n n .nnnn ?r^.nn P P 26 50 .gogg IGG .GGGG 2QG.GGQC-. 27 sa .GGGG 2GG.GCGG ZSCQCGG 23 5C .GCGG 3CG .GGGG 2QG.GGaa 29 5G .nncG 3 1G.GGGG 2 G a . G G U C 3Q 5G .GaaG 32G.CGQG 2aa.aaGG 31 iaa .GGGG .GGGG 2GG.GGGC 32 iGG .GOGG IGG. GGQG 2 G a . C G G ; 33 1GC .GQGC 2GG..QCGG 2 a G . G G G G " 33 Output of Example Problem Using FEMESH 34 1GG« GCOO 3GG, .OGGO 2 G G . o o a 35 LOG', a ooo 3 1G , G 2 c g . a a g c 36 IGG. gcog 32G ,GGCO 200.0000 37 GOOG .caac i o a . c a a a 33 CGQO IGG .0000 400 . GGGO 39 coaa 2GG .GGOG 4GC . GOOG 40 GCGG 3GG .cccc 4CC. GOOG U 1 f .1 f* n Li u u U 3 10 .GGGC ^00.0000 42 GGGO 3 20 .GGGC 400. GCGG 4 3 f' Vt ' GGGC .OCCC 40G..0aG0 44 50. aacc IGG ,OOCC 400.0000 45 5G . GOOG 2CG .GCGG ^OG .CCOC 46 5Q. .uOGC- 3GC .GGOG 4 00.0000 47 5G i ijGuu 3 1G .GGGC .GGGC 4 • . G 43 50. GCGG 3 20 4CG .CGGG uQ LOG GGCG . a o c c arc H o '1 n 50 IGG .GCGG IGG .GGCG 51 IGG .GGGC 2CG .0000 . GCGG u ; ' n n n n h "* '— >-j » U -j w Uj 52 IGG . C G u 3GG ti n n " "■ n ~ " J tj • ^- ^ L-. w 53 IOC . caaa 31G. GGOG 400. GOOG Su 1 HG . nnnn 3?n nnnr, unn.nnnn « 55 GOOG .aoao 60 0.0000 • Sft nnnn _ LOU .nnnn 6 0.0000 . 57 GGGO 200 .0000 60G.000C 53 ccoc 3.C_C ► ac.ac 600.0000... 59 aoao 310 .OGGO 6 a c . g a o a ^n nnnn 3 2.2- .nnnn 600 . nnnn 61 50, ,G000 .oaaa 60Q.G000 A? sn nnnn \ n n .nnnn f*nn .nnnn 63 SO ► aaca 2CG .GOGO 6 o c . a a o a ^a 50 .nnnn vGG-.C 600.0000 65 50 ,oaaa 31G .aocc 600 .GGGO r> 6 sn .nnnn 3 7 n .nnnn ann.nnnn 67 100. .caaa .GGOO 6oa.aaoo ^A 1 nn .nnnn i nn .nnnn h n n , -n n n n 69 1GQ .oaoc 200 .gooc 6oa.Gooa 7n i nn .nnnn ^nn. .nnnn ^nn.nn n n i 71 100 .oaaa 310 .0000 6 g a . a o o o ; 7? 1 nn .nnnn .320. .nnnn r,nQ.nnn n ' 34 Output of Example Problem Using FEMESH ELEMENT GENERATION 3E.3U175 I 19 25 7 2 20 26 3 1 i ? ?<-< ?i. a 7 7 ' 7 ~ a i - n 21 27 9 4 22 25 10 1 1 a a 77 7a i P c 7 ' ?<3 i i 7 1 p 5 2 3 29 11 6 24 30 12 3 1 a 7 7 c 7 i 1 7 * 7i. 7? 1 u i i p 5 26 32 14 9 27 33 1 5 1 i a 77 7 7 i P 7 3 * 4 i * 1 i p 10 23 34 16 11 29 3 5 17 2 1 a 1 i 7 = 7 C l 7 i 7 7 P "^ 1 2 7 i n 19 37 4 3 25 2D 33 44 25 1 1 ?n 7 3 a u / -» 7 i 7=s ^ = , ~ 7 i i n 21 39 45 27 22 4 4o 2 5 1 1 G 7? tip UA -> 2 7? 4 1 (I 7 7a 7 i p 23 41 47 29 2^ 42 43 ^ vj 3 1 a ?p a 7 uo 7 1 76 ua -n 77 1 1 p 26 44 50 32 27 4 5 51 .13 1 1 ^ 7 u = =; i 7 7 75 u ~ - ? " -!• 1 1 p 23 46 52 34 29 47 53 3 5 2 1 a 7<3 47 S 7 I = 7P 4 = S 4 62 44 1 1 1 (7 37 55 6 1 4 3 33 56 7A So o7 U 4 7G =;7 o T 4 =; i 1 n 39 57 63 45 tl o 4 u 53 64 46 T 1 a UP t; 3 ~ 4 u A U, 1 c c o =; 4 7 7 i p 4 1 59 65 47 42 60 66 43 3 1 u ~ £ 1 o7 49 4 a o 7 -a = n i 1 p 44 62 63 50 45 63 69 51 1 1 45 63 69 5 1 Uo 6 4 70 71 - 5 2 53 1 2 1 a 46 64 70 52 47 65 a 47 .. 6 .5 . 7! S3 u* 66 7 7 =; u 3 1 p 35 CHAPTER 4 OPERATING INSTRUCTIONS FOR ANSYS 4.1 WAVE FRONT SOLUTION AND LIMITATIONS The ANSYS program uses the wave front direct solution method for the system of simultaneous linear equations which are developed by the matrix displacement method. The frontal direct solution gives results of high accuracy in a minimum of computer time. There is no "band width" limitation in the problem definition . However, there is a "wave front" restriction . The "wave front"" " restriction depends on the amount of core storage available for a given problem . Up to 576 degrees of freedom on the wave front can be handled in a large core. An optional 1152 wave front is avail- able on very large computers. However, it is recommended not to exceed the 571 wave front if the CYBER 176 (CDC 7600) computer is used. The wave front limitation tends to be restrictive only for the analysis of three-dimensional structures or in the use of ANSYS in small computers. There is no limit on the number of elements used in a problem, but there is a limit on the number of elements which consist the wave front. The number of equations which are active after an element has been processed during the solution procedure is called the wave front of that point. For a banded solver, the band width is minimized by paying close attention to the ordering of the nodes. Alternatively, in the wave front procedure, the ordering of the element is crucial to minimize the size of the wave front. A degree of freedom becomes active when an element containing that degree is processed. That degree of freedom remains active in core until all elements containing that degree of freedom have been processed. Therefore, the element cards must be arranged in such a way, so that the element for which each nodal point is mentioned first is as close in sequence to the element for which it is mentioned last. The wave front must sweep through the model continuously from one end tcTThe other in the direction wmch has the largest number ot nodT points . The assembled matrix expands and contracts as nodal points make their first and last appearance in the element specifications. The optimum wave front for a simple line element model is a point; for a two-dimensional solid or plate element is a line of nodes; and for a three-dimensional solid, element is an area of nodes. An estimate of the wave front size can be made by multiplying the number of nodes in the wave front by the number of degrees of freedom per node. For example, consider the model shown in Fig. 3.1. The xz plane has the lesser number of nodes (3x4 = 12). Thus, the elements should be specified along the upper xz plane in the y direction. The new ordering of the elements is shown in Fig. 4.1. 36 If the elements described above have three degrees of freedom per node (say ux, uy, and uz), the maximum wave front size is approxi- mately 12x3 = 36. Often, it is convenient to generate elements with FEMESH in an order that is not the best for an optimum wave front. If so, elements may be internally reordered by ANSYS using the Fl cards. The Fl cards are called into the full ANSYS problem by inputting ' KORDER = 1 (column 78 of the C2 cards). A list of nodal points defining where the element reordering is to start is input on the first Fl card set. Additional lists may be defined to allow the user to guide the wave. The starting list usually consists of one node for a line element model , a line of nodes for an area element model, or a plane of nodes for a volume element model. There is a limit of 25 Fl cards or 1000 nodes, whichever comes first. All elements attached to the first node in the list are defined first, then all elements attached to the second node are defined next, etc., until all elements attached to all nodes input on the first Fl card set (but not on later Fl card sets) are defined. This procedure is then repeated with the new set of nodal points brought in with the previously defined elements. If, during the course of reordering, an element would bring a node that is defined on a later Fl card set, that element is omitted until later. This feature allows the user to guide the wave front. The element reordering, using the Fl cards of the mesh shown in Fig. 4.1 from the mesh shown in Fig. 3.1 (generated by FEMESH), is presented in Table 4.2. It is recommended not to use the Fl cards if interface elements (connecting the slab to the subgrade) are used. It is rather easier to reorder the elements by hand. 4.2 DATA INPUT INSTRUCTIONS Abbreviated ANSYS input instructions and the proper formats are included in this section. Specific quantities to be used for some of the variables are given in the Element Library (Chapter 5) for the various element types which to be used. Standard FORTRAN conventions are used for the input quantities. Variables with first letters from I to N are integers and must be riant justified (ending in the right- most column) in the specified field . No decimal point should be in- cluded. Variables with other first letters are floating point numbers and may be placed anywhere in the field. Floating point numbers should have the decimal point input. The exponent, if any, must be right justified in the specified field . No data should be punched on the cards in other than the specified fields. A blank input is treated as a zero or as a default option where indicated. Data cards must be in the order defined, and no add- itional cards (except for comment cards) are allowed. Comment cards may be inserted freely in the data deck. A comment card is identified by the characters C*** in columns 1 through 4. The remainder of the card is used for any comment that the user wants to have printed out along with the data input listing. All alphabetic labels (UX, FY, EX, END, etc.) must be left justified in their four space fields . Card sets requiring sentinel caras for termination are identified in the 37 tables. A card having only a -1 in columns 5 and 6 may be used for any sentinel card. All geometric input angles are in degrees and out- put rotations are in radians. Right hand coordinate systems are used throughout except where specifically noted . 4.2.1 ANSYS Input Data for "Static Analysis (ANSYS/Rey. 2) CARD CI COLUMN(S) TITLE CARD 1-30 VARIABLE IHEDD MEANING ACCOUNTING CARD 1-16 18 NAME NONOTE Title for output. If columns 77-79 are left blank and a comma punched in col- umn 80, the title may be continued on the following card. No limit. (Optional) User Identification Name. - Print notes (new features, modifi- cations, announcements, etc.) at end of solution. 1 - Suppress printout of notes (con- tinued use not recommended). (Not Available) 25-32 IACCNT (System Option) Account Number 37-42 IEQRQD (Optional) Maximum number of equations in wave front (to check for adequate core storage) . 75-30 ICORE (System Option) Core size parameter. Note - If no values are input, a blank card is still required. ANALYSIS OPTIONS 1-4 7 11-12 NSTEPS K20 KTB 16 K15 Number of load steps (one set of L through Q cards per load step) (-NSTEPS for an input data check run). - Static analysis - No element real constant table defined 1 - Define up to 8 element real constants per table entry (Card D2). N - Define up to N (for N greater than 8) element real constants per table entry (Card D2). - No nodal force output. 1 - Calculate and print out nodal forces for each element and tab- ulate reaction forces at specified displacement constraints. K2Q=0 38 CARD COLUMN(S) CI (cont.) 16 C2 VARIABLE K15 MEANING 18 K17 - Print out reaction force tabula- tion only - Boundary conditions (.Cards N, 0, P, and Q) are linearly inter- polated within a load step. The full boundary conditions (as input) are used in the last iteration of the load step. - Boundary conditions are step changed at the first iteration to full values defined in the load step. 22 K23 74-75 KPROP N - No energy printout. - Calculate and print out elastic strain energy for each element. - Use polynomial material property equations. - Use linear interpolation in all material tables, up to N points per table (24 max.) . ANALYSIS OPTIONS (CONTINUED) 1-12 TREF Reference temperature for thermal expansions. 13-24 TUNIF Uniform temperature (used if no other temperatures are specified). ELEMENT TYPES - One card for each element type. End card set with an 1=0 card. 2-3 I Element type number between 1 and 20) . (arbitrary, 5-6 J Stiffness subroutine for this element. (A will cause this element type to be ignored). 7 8 9 10 11 12 KEYSUB(IB) KEYSUB(IA) KEYSUBU) KEYSUBC2B) KEYSUBC2A) KEYSUB(2) Parameter KEYSUBU B) Parameter KEYSUBU A) Parameter KEYSUBU ) Parameter KEYSUB(2B) Parameter KEYSUB(2A) Parameter KEYSUB(2) for this subroutine for this subroutine for this subroutine for this subroutine for this subroutine for this subroutine 14-15 18 KC If J-0, enter for KC the stiffness sub- routine number of the element type being ignored. INOTPR If 1, suppress all stress and force printout for this element type. (Return to next D card) K2Q=0 39 VARIABLE MEANING CARD COLUMN(S) D2 ELEMENT REAL CONSTANT TABLE - Clnclude this card set only if KTB is greater than Q on Card CI. The D2 cards may be repeated to form a table. End table with a blank (or 0.0 in the first field) card).. Element real constants (as given for element stiffness subroutine. Input constants in the same order as given. , Several cards may be required for 71-80 RC(8) each table entry. Additional constants on cards are not used) . 1-10, RCCD 11-20, RC(2) 21-30, RC(3) E El If a +00000 is punched in columns 1-6 and the rest of the card is left blank, suppress the element constant table printout. If -99999, cancel the suppression. If a +99999 is punched in columns 1-6 and a real number (D.) is input for RC(2) , this card represents D blank table entries. (Return to next D2 card) ELEMENT DEFINITION CARDS - one card set (El, E2) for each element - end with an I=-l card. ELEMENT DESCF.IPTION 1-6 I 7-12 13-18,19-24, 25-30,31-36, 37-42,43-48 49-54 K, L, M, N, 0, P MAT Number assigned to Node I on element (first node). If 99999, suppress element printout. If -99999, cancel the suppression. Number assigned to Node J on element (second node, if any) . Other node numbers, if required. Material number of this blank) . element (1 if 55-60 61-66 ITYPE ITABLE Element type number for this element (1 if blank). (Refers to element types defined on D cards). - Element real constants, if any, are included on the next card (Card E2) K. - Element real constants are included at entry number K of the D2 card set. K2Q=0 40 CARD COLUMN (S) VARIABLE MEANING El (cont.) (The following three parameters are required only for ■ or second level element generation). 67-72 IiNUM If positive (first level generation), INUM is the total number of element sets generated (including the spe- cified set). The elements input on this and the next NEL-1 El. cards form the specified set. If negative (second level generation), -INUM is the total number of element groups generated (incl uding the NEL elements in the defined group). The defined group may include separately specified and/or first level generated elements. Columns 1-66 should be left blank. 73-75 NINC Number by which to increment each element node number to generate suc- cessive element sets or groups. (Assumed 1 if left blank). 76-78 NEL Number of elements in a specified set or a defined group to be repeated (assumed 1 if blank) . Element limit per set = 960/N (where N=8 or KTB, if KTB (Card CI) is greater than 8). No element limit per group. 79-8Q KNEXT If positive, the tape unit for add- itional element input data (defaults to the current input file). If -1, all of the following elements have INUM added to each node number. E2 ELEMENT REAL CONSTANTS - (Include this card set only if the element has required real constants and if I i ABLE (on the preceding El card) is zero or blank). 1-12, RC(1) Element real constants i^as given for 13-24, RC(2) element stiffness subroutine. Input 25-36, RC(3) constants in the same order as given. 37-48, RC(4) Several cards may be required for each 49-60, RC(5) table entry. Additional constants on 61-72 RC(6) cards are not used). (Return to next El card) K20=0 41 CARD COLUMN(S) VARIABLE MEANING F NODE POINT LOCATIONS - One card for each node specified - and with an I--1 card. * 1-6 I If positive, I is the node number being defined (not a ]] numbers need to be used) . If zero (or blank), this card is used to define a local coordinate system. If negative, this card is used to define second level nodal point gen- eration. -I is the node number in- crement between successive nodal point groups. If 99999, suppress nodal point print- out. If -99999, cancel the suppression. 7-3 KCS **"* If I is not zero **** - Nodes input (or generated in global cartesian coordinates. 1 - Nodes input (or generated) in globa" cylindrical coordinates. 2 - Nodes input (or generated) in global spherical coordinates. N - Nodes input (or generated) in local coordinate system N (N greater than 2). ***** If I is zero *"** - A local cartesian coordinate system is being defined. 1 - A local cylindrical coordinate system is being defined. 2 - A local spherical coordinate system is being defined. 9-10 KFILL If I is positive **** - No first level nodal point genera- tion. N - Fill in nodes between the previously specified node and this one, incre- menting node numbers by N and linearly interpolating the coordinates (First level nodal point generation). (N must be positive) . K20=0 42 CARD F (cont. COLUMN(S) 9-10 VARIABLE KFILL (cont. ) MEANING *** If I ts zsro *** N - The local coordinate system being defined is identified as coordinate system number N (N greater than Z) . *■*■* N - If I is negative X'M jfc 11-12 !<NEXT The number of nodal points in the group to be repeated (defined on the following F cards). (Second level nodal point generation). *** If I is positive *** N - The tape unit number for additional nodal point input data (defaults to the current input file). *** If I is zero, KNEXT is not used *** *■*■* N - *-** If I is negative *** The total number of nodal point groups generated (including the defined group). (Second level nodal point generation). Special Combinations *"*"* If KNEXT=-1, all of the following node numbers have I (positive or negative) added to them. All other parameters on the card should be left blank. For defining nodal points use the appropriate node description column below. The THXY, .., THRP inputs are for nodal coordinate rotation. All angles are input in degrees. Use 3-0 input if a 3-0 element is included in the D card set. For local coordinate system definition use Column 3 for origin translation and coordinate system rotation. For second level generation, inputs are incremental values. Increments and nodal- points must be specified in the same coordinate system (KCS). 2-0imensional Rectangular Polar 13-24 25-36 37-48 49-60 61-72 73-80 X Y THXY R THETA THRT (Return to next K20=0 Cartesian X Y Z THXY THYZ THXZ F card) 3-0imensional Cylindrical R THETA Z THRT THTZ THRZ Spherical R THETA PHI THRT THTP THRP CARD CQLUMN(S) VARIABLE MEANING H MATERIAL PROPERTY DEFINITIONS - the H card set CHI , H2) may be repeated. End with a LABEL=END card. HI -MATERIAL PROPERTY EQUATIONS 1-4 LABEL LABEL identifying the property EX EY EZ ALPX ALPY ALPZ NUXY NUYZ NUXZ DENS MU GXY GYZ GXZ COPR NOPR END (Note - All labels are left justifies) (Only properties required by element material descriptions need be input. In addition, for isotropic materials, only the X (or XY) property label need be input) . 5-8 MAT Material number (assumed 1, if left blank). 12 KEY - Polynomial coefficients are input on this card. 1 - A curve must be fit to the set of temperature vs. property data points listed on the following H2 cards . 2 - Fit curve as described for KEY=1 and print out the fitting equation coefficients. 3 - Use linear interpolation in all material property tables (input table on H2 cards). (Note, if KEY=3 for any material, it must be 3 for all materials). 13-24 CO Constant term in the property polynomial equation. Coefficient of linear term in equation. Coefficient of quadratic term. Coefficient of cubic term. Coefficient of quartic term. H2 MATERIAL PROPERTY TABLE - (Included only if KEY is greater than zero on previous HI card) First card - 1-12 POINTS Number of temperature ys. property points in table. If KEY=1 or 2, at least 6 property points are required. If KEY=3, the number of points must not exceed the KPROP value input on Card CI. K20=0 44 25-36 CI 37-48 C2 49-60 C3 61-72 C4 CARD COLUMN(S) VARIABLE MEANING H2 (cont. ) "I 3 " 24 TSTART Temperature corresponding to first property value input [required only if DELTAT is greater than zero). 25-36 DELTAT Constant value by which, temperatures are incremented. Temperatures corre- spond to property values input on the next card(s) . Following cards - If DELTAT=0.0 (or blank), three temperature- property pairs may be input per card. Tem- peratures must be input in ascending order. If DELTAT is greater than zero, six properties may be input per card. Properties correspond to temperatures generated on first H2 card. (Continue table on as many cards as required, Format (6E12.2)) (Return to next HI card after table is complete). L-Q The following load cards (L-Q) are repeated NSTEPS (Card CI) times unless the repeating sets are terminated with a KDIS= <3 9 card before the last expected (NSTEPS) set. L LOAD STEP DEFINITION 1-3 KDIS 1 - Define new values for displacement, force, and pressure boundary condi- tions. Formulate new stiffness matrix. Zero all nonlinear terms and previous boundary conditions. - Use the previous displacement, force and pressure boundary conditions (do not include N, 0, or P card sets). Reformulate stiffness matrix. Continue nonlinear analysis. -1 - Change some of the previously defined displacement, force, and pressure boundary conditions (include changed values and N, 0, and P card set terminators). Also use unchanged previous bounc^ry conditions. Re- formulate stiffness matrix. Conti- nue nonlinear analysis. 2 - Same as KDIS=1 except use previously formulated stiTfness matrix (speci- fied displacement constraints (on N cards) must be reseated (and all zero) ) . K20=Q 45 CARD COLUMN(S) L 1-3 (cont. ) VARIABLE MEANING kdis -a (cont. ) 4-6 KTEMP 99 - - 1 - 2 - 3 - -N - Same as KDIS--1 , except use previ- ously formulated stiffness matrix Cspecified displacement constraints must remain zero) , Terminate the load card sets before the last expected set. An R or S card must follow. Set all temperatures to TUNIF (Card C2). Read in element temperatures on the Q cards for all elements. Read in nodal point temperatures on the Q cards. Use temperatures from previous load step. Use the temperatures calculated in the Nth cumulative iteration (file TAPE4) of a previous ANSYS heat transfer solution. 7-9 NITTER 10-12 NPRINT M The number of sub-step (or iterative) calculations to be done this load step (defaults to 1). Note, boundary con- ditions are linearly interpolated if ,K17=0. If NITTER is negative, use covergence options (step boundary con- dition change imposed). Frequency of printout of stress, force, and displacement results - only every NPRINT iteration is printed out, begin- ning with iteration NPRINT. If zero or blank, suppress all printout for this load step . If negative, suppress boundary condition input printout only, For a negative value of NITTER, if NPRINT- NITTER , print the converged (or last) iteration. If NPRINT > NITTER , suppress all solution print- out. ADDITIONAL LOAD, PLOT, AND PRINT DEFINITION CARD The following four parameters may be used if more than three space fields are needed for the corresponding parameters on the L card. 1-6 7-12 KDIS If non-zero, use instead of the value on Card L. KTEMP If non-zero, use instead of the value on Card L. K20=0 46 CARD COLUMN(S) VARIABLE MEANING M (cont.) 13-18 NITTER If non-zero, use instead of the value on Card L. 19-24 NPRINT If non-zero, use instead of the value • on Card L. N DISPLACEMENT DEFINITION CARDS - The N cards may be repeated. End with a LABEL=END card. 1-6 I Node number at which displacement is specified. If 99999, suppress displacement printout. If -99999, cancel the suppression. If -2, add 12 to all the following nodes, 7 IKEY If -j delete this displacement specifi- cati on . 8-11 LABEL Direction of displacement. (In nodal coordinate system) UX UY UZ ROTX ROTY ROTZ PRES END 13-24 DISP Value of displacement at this time (Radians for totations). 37-42 12 If 12 is greater than I (for I positive), 43-48 15 all nodes from I through 12 in stpes of 15 have this specified displacement (.15 is assumed to be 1 , if left blank) 51-54, LABELS (5) Additional direction labels for which 57-60,63-66, this displacement value applies at 69-72,75-78 this node. (Return to next N card) Q FORCE DEFINITION CARDS - The cards may be repeated. End with a LABEL=END card. 1-6 I Node at which force acts If 99999, suppress force printout If -99999, cancel the suppression If -2, add 12 to all the following nodes. 8-11 LABEL Direction of force. (.In r\oda] coordinate system) FX FY FZ MX MY MZ FLOW END K20=0 47 CARD CQLUMN(S) VARIABLE MEANING (cont. ) 13-24 FORCE Value of the force at this time. 37-42 12 If 12 is greater than I (for I positive), all nodes from I thru 12 in steps of 15 have this specified force (15 assumed to be 1 if left blank). (Return to next Q card) P PRESSURE DEFINITION CARDS - The P cards may be repeated. End with a blank (or 1=0) card. Pressures act in the element coordinate system. See Table 4.J.1 for pressures available for element type J. 1-6 I Element upon which pressure acts If 99999, suppress pressure printout. If -99999, cancel the suppression. If -2, add 12 to all the following elements. 7-12 IFACE Face of element on which pressure acts. (If a super-element, IFACE is the load vector number) . 13-24 PRESS Value of the pressure at this time. (If a super-element, PRESS is the scale factor for load vector IFACE). 37-42 12 If 12 is greater than I, all elements from I through 12 in stpes of 15 have this pressure on this face (15 is assumed 1 if left blank). (Return to next P card) q TEMPERATURE DEFINITION CARDS - (Include this card set only if KTEMP-1 or 2 on Card L). Element temperature format (used if KTEMP is 1). One specifica- tion is required for each element, in the same order that the elements are specified. If KTEMP=2, use the node temperature format. 1-8 Tl First temperature for this element. K2Q=0 48 CARD CQLUMN(S) VARIABLE MEANING Q ■ 9-16,... T2,.,. Second temperature, etc. (cont.) .;, 57-64 ...,T8 (Note - Fluences are also Input where applicable) , 65-72 INUM If or 1, one element has this set of. temperatures. If N, the neat N elements (.counting this element) have these temperatures. 73-74 KNEXT If positive, subsequent temperature input is to be from tape KNEXT (defaults to the current input file). 76 KTCONT - All temperatures and fluences to be specified are contained on this card. 1 - Additional temperatures and fluences continued on next card. Note - If KTC0NT=1 , T9 through T16 should be input on the next (second) card. The continuation card format is the same as the first card except that INUM and KNEXT are not used. Values not input are assumed to be zero. If a +99999 is punched in columns 1-6, suppress the element temperature printout. If -99999, cancel the suppression. (If all element temperatures have not been specified, return to next Q card). Nodal point -temperature format (used if KTEMP is 2). Nodal temperature specification cards may be repeated. Nodal temperatures not specified are set equal to TUNIF (Card C2). End nodal temperature set with an I=-l card. 1-6 I Node number at which temperature is specified (if -1, end of nodal tem- perature input) . If 99999, suppress nodal temperature printout. If -99999, cancel the suppression. If -2, add 12 to all the following nodes. Specified nodal temperature. Specified nodal fluence. If 12 is greater than I (for I positive), all nodes from I through 12, in steps of 15, have this temperature (15 is assumed to be 1 if left blank). K2Q=0 49 13-24 TEMP 25-36 FLUEjNCE 37-42 43-48 12 15 CARD CQLUMN(S) VARIABLE MEANING Q ( cont -) (Return to next Q card) (Return to neat L card tf another load step is to be defined). S END OF DATA DECK CARD 1-6 FINISH The word FINISH is punched in Columns 1-6 of the last card of a problem data deck. Another problem data deck (oeginning with Card A) may follow. K20=Q 50 Oftentimes for real life problems, the engineer will have to use the 3rd Revision of ANSYS (Extended Core Version). To go from the 2nd Revision to the 3rd one, set NSTEPS - Q [solution problem} or NSTEPS 3 -1 (model check problem) on card CI and finish with L-Q card sets with a KDIS-END card. 4.2.2 ANSYS Input Data, for w«t Transfer Analysis (ANSYS/ Rev. 2) CARD COLUMN (S) VARIABLE MEANING A B TITLE CARD - See section 4.2.1 for data input instructions. ACCOUNTING CARD - See section 4.2.1 for data input instructions. CI ANALYSIS OPTIONS 1-4 NSTEPS 6-7 K20 1-12 KTB 1 N 16 K15 1 2 18 K17 32 KAY(2) Number of load steps (one set of L through Q cards per load step). (-NSTEPS for an input data check run). -1 - Heat Transfer analysis. No element real constant table defined. Define up to 8 element real con- stants per table entry (Card 02). Define up to N (for N greater than 8) element real constants per table entry (Card D2). No nodal heat flow rate printout. Calculate and print out nodal heat flow rate for each element and tabulate heat flow rates at speci- fied temperature constraints. Print out heat flow rate tabulation only. Boundary conditions (Cards N, 0, P, and Q) are linearly interpolated within a load step. The full bound- ary conditions (as input) are used in the last iteration of the load step. 1 - Boundary conditions are step changed at the first iteration- to the full values defined in the load step. - First order integration for trans- ient solutions. <20=-l 51 CARD CI (cont. ) COLUMN(S) 32 74-75 VARIABLE KAY(2) (cont. ) KPROP MEANING 77 K18 1 - Second order integration for trans- ient solutions (recommended) (required for convergence or optimization procedures). - Use polynomial material property equations. N - Use linear interpolation in all material tables, up to N point per table (24 max. ) . - Nodal coordinate directions rotated for nodes input in global cylin- drical and global spherical coordi- nates (nodal x-axis is along input radius unless otherwise specified on F card. C2 ANALYSIS OPTIONS (CONTINUED) 13-24 49-54 NUMEL 55-60 MAXNP 61-64 KRSTRT 65-68 TOFFST 69-75 TUNIF Used only if KDIS=1 . If so, all nodal temperatures , the temperature boundary conditions (Card N) and the bulk tem- peratures (Card P) at the beginning of the load step are set to TUNIF. Also temperature dependent material properties are evaluated at TUNIF for the first iteration. Number of elements (required only for restart). iMaximum node number (required only for restart). The last load step already done, (restart key) . Degrees between absolute and of temperature system used (required for radiation) . TRSTRT Time at end of run to be continued (required only for restart}. ELEMENT TYPES - See Section 4.2.1 for data input instructions Note, the INOTPR parameter is used to suppress all heat flow printout for this element type. K2Q=-1 52 CARD COLUMN(S) VARIABLE MEANING D2 ELEMENT REAL CONSTANT TABLE - (Include this card set only if KTB is greater than on Card CI . See section 4.2.1 for data input instructions) . E ELEMENT DEFINITION CARDS - See Section 4.2.1 for data input instructions. F NODE POINT LOCATIONS - See Section 4.2.1" for data input instructions H .MATERIAL PROPERTY DEFINITIONS - See Section 4.2.1 for data input instructions. Note, the list of structural property labels (Cols. 1-4) should be replaced with the following thermal property identification list. KXX KYY KZZ DENS C HF OHMS VISC EMIS NOPR GOPR END L-Q The following load cards (L-Q) are repeated NSTEPS (Card CI) times unless the repeating sets are terminated with a KDIS=99 card before the last expected (NSTEPS) set. L LOAD STEP DEFINITION 1-3 KDIS 1 - Define new values for temperature, heat flow, and convection boundary conditions. Formulate new conduc- tivity and specific heat matrices. Zero all transient terms and pre- vious boundary conditions. - Use the previous temperature, heat flow, and convection boundary con- ditions (do not include N, 0, or P card sets). Re- formulate matrices Continue transient analysis. -1 - Change some of the previously de- fined temperature, heat flow, and convection boundary conditions (include changed value's and N, 0, and P card set terminators). Also use unchanged previous boundary conditions. Re-formulate matrices. Continue transient analysis. K20=-l 53 CARD COLUMN(S) L 1-3 (cont.) 4-6 VARIABLE KDIS (cont. ) KTEMP MEANING 99 - - 1 - 3 - Terminate the load card the last expected set. card must follow. sets before An R or S Set all internal heat generation rates to 0.0. Read in element internal heat gener- ation rates on the Q cards for all elements. Use heat generation rates from pre- vious load step. 7-9 NITTER 10-12 NPRINT M The number of sub-step (or iterative) ■ calculations to be done this load step (defaults to 1 ) . Note, if K17=0, boundary conditions are linearly inter- polated. If NITTER is negative, use steady-state convergence (step boundary condition change required) or transient optimization procedure. Frequency of printout of heat flows and temperature results - only every NPRINT iteration is printed out, beginning with iteration NPRINT. If zero or blank, suppress all printout for this load step ! If negative, suppress boun- dary condition input printout only. For a negative value of NITTER, if NPRINT= NITTER , print the converged (or last) iteration. If NPRINT > NITTER , suppress all solution printout. Time characterizing the end of this load step (If TIME is 0.0, blank, or less than the time of the previous load step, a steady-state solution is done). ADDITIONAL LOAD, PLOT, AND PRINT DEFINITION CARD The following four parameters may be used if more than three space fields are needed for the corresponding parameters on the L card. If non-zero, use instead of ' the value on Card L. If non-zero, use instead of the value on Card L. If non-zero, use instead of the value on Card L. If non-zero, use instead of the value on Card L. K2Q=-1 13-24 TIME 1-6 KDIS 7-12 KTEMP 13-18 NITTER 19-24 NPRINT 54 CARD COLUMN(S) VARIABLE MEANING N TEMPERATURE DEFINITION CARDS - The N cards may be repeated. End with a LABEL-END card. 1-5 I 7 3-11 13-24 37-42 43-48 IKEY LABEL TEMPER 12 15 Node number at which temperature is specified. If 99999, suppress temperature printout. If -99999, cancel the suppression. If -2, add 12 to all the following nodes. If -, delete this temperature specifica- ti on . Input one of the following words (left justified) . TEMP PRES VOLT END Value of temperature (etc.) at this time. If 12 is greater than I (for I positive), all nodes from I through 12 in steps of 15 have this specified temperature (15 is assumed to be 1 , if left blank). (Return to next N card) CONVECTION DEFINITION CARDS - The P cards may be repeated. End with a blank (or 1=0) card. 1-6 I 7-12 13-24 IFACE HCOEF 25-36 TBULK Element upon which convection acts. If 99999, suppress convection printout. If -99999, cancel the suppression. If -2, add 12 to all the following elements. Face-^f element on which convection acts. If a. super-element, IFACE is the load vector number. Value of the film coefficient at this time. Note, if KDIS-1 , the film coefficient at the beginning of this load step is also set to this value. If -N., use HF vs. TFILM equation input for material N on the H cards. If a super-element, HCOEF is the scale factor for load vector IFACE. Bulk temperature of adjacent fluid at this time. K2Q=-1 55 CARD COLUMN(S) VARIABLE MEANING P TBULK (cont. ) (cont.) 37-42 12 If 12 is greater than I (for I positive), "43-43 15 all elements from I through 12 in steps of 15 have this convection on this face (15 is assumed to be 1 if left blank). (Return to next P card) Q HEAT GENERATION RATE DEFINITION CARDS - (Include this card set only if KTEMP-1 on Card L. One speci-' fi cation is required for each element, in the same order that the elements are specified) . 1-3 HTGEN Internal heat generation rate for or CI this element. 9-16, C2,— Constants defining polynomial equation — ,57-64 — ,C8 for variable heat generation rate (applicable to STIF71 elements). 65-72 INUM If or 1 , one element has this rate. If N, the next N elements (counting this element) have this rate. 73-74 i KNEXT If positive, subsequent heat generation rate input is to be from tape KNEXT (defaults to. the current input file). If a +99999 is punched in Columns 1-6, suppress the internal heat generation rate printout. If -99999, cancel the sup- pression. (If all element heat generation rates have not been specified return to the next Q card). (Return to next L card if another load step is to be defined) S END OF DATA. DECK CARD 1-6 FINISH The word FINISH is punched in Columns 1-6 of the last card of a problem data deck. Another problem data deck (begin- ning with Card A) may follow. •K20=-l 56 4.2.3 ANSY5 Input Data for Thermal Stress Analysis The thermal stress is equivalent to the static analysis except as follows: 1. Save file TAPE 4 from heat transfer analysis. 2. Assign file TAPE 4 to thermal stress analysis. 3. Set KTEMP=-N (read temperatures fo the Nth iteration of previous heat transfer solution from file TAPE 4). Table 4.1 Element Reordering Instructions FIELD COLUMNS VARIABLE MEANING CARD Fl **** ELEMENT REORDERING INSTUCTIONS— Use as many cards as necessary to define a starting wave set. Use additional cards to define additional starting wave sets. End Fl card set with and Nl= END card. First node, second node, third node, etc., on starting wave. Continue on additional cards if necessary (Format 1216). 12 67-72 N12 Blank fields are ignored. End starting wave list with a -1 node number. 1 1-6 Nl 2 7-12 N2 3 13-18 N3 (Return to next Fl card) 57 a SJ <S3 S- a C5 s_ oj s. o <u CM cu 2-3 3j ' 3 3 S _j m :q la COI H i>— ! :cni Si! a\ -; £li- 1 -.-■I j >■■ - l ! r 1 ; i»i -' i r 1 1 !«i 5. J) 1 ! 1 i*i 3? S| 1 - h 5) 1 1 . \i V =1 - :• 1 : ! I , L-, ^ 1 i i ! l ill 1 l;j SI 1 i St =1 SI ;)-. | 1 i 1 1 jsi 21 1 i 1 i r i : , Ui SI : 1st 31 1 : : ill HI 1 i i ! lal 31 > i I SI 31 ■ II u : _1 ;1 St ^ 1 i 51 i r.. 1 i >SI i =1 i Ui | i N il i l i i 1 V i r I ; jsi sj r < i 1 =1 ' ! i I i" =r^ " " i l i 1 1 ■ |s| 2) I ! ! 1 \a'i 5| ; : 1=1 SI 1 1 1 : i i Ui SI | 1 ! : I = i =! 1 i ; "! ' l=i =1 1 i i ; -i 31 i SI SI ! : i IS! 31 1 1 i j«j SI i j - j SI l ■s| SI 1 !sl si I sj si 1 '-! S| i ! 1 Z3°i S| 1 i '•■ i| 1 : i • -'i S| ! 1 1 : 1 ; i i-l *l i -1 i 1 I 1 I s ! 1 i <~\ M ! i Ul =r~ 1 i 1 i ! i r-\ SI 1 ! ! ! : l i i ; : i 1 I s ! =i i ' '=1 =ii'. ! i "' ' .31 =i- i 1=1 »! i i ■ ! 1 ! i i l«| SI I 1 ! i ; i ,= i 81 i ; : i i i !s| sj i i i i 1 'SI = 1 i i ; 1 i i ~i = 1 1 ' ■ 1 : ! i 1 j ! ill i i s ! S) i ! i 1 l i 1 i i-i =1 | . : • i i ! i I s ! [ l ! i i i !ai ! =j r I ■z\=. *j f ; ii ! 1 i ; ; |*|i St 1 ' f ! 1 ! I : i |S|? si I y ' i ' l j_ i i i |H| 1 j ; ! l=|j =i- i l s U ! ; i -f— ' \-U =t ■! 1 j | i . r is i ! i |=|t i ,1 I , 1 : I ! — H§ .1 1 ! i ! ' i ■ "'* - i 1. i . I : : j i 1 '-I.: r»c5t-icj!cvji^-c3v — ' -*\- , pjaSto^ssij I — -- i-iJ : i ■! l-ll x * -1 CJ 3 - -1 , i "3>" . -., . ! — :m-( LUl ■ -'. 58 Y Sk A A A A A /\ = Element Number NX=3 NY-6 NZ=4 ny)nz)nx NOTE THAT ThFoRDERING OF THE NOOES IS THE SAME AS IN FIGURE 3.1 WAVE FRONT=(NX)(NZ) (DEGREES OF FREEDOM PER NOOE) Figure 4.1 Example of Element Reordering to Minimize the Wave Front 59 CHAPTER 5 ELEMENT LIBRARY OF ANSYS 5.1 ELEMENT SELECTION Table 5.1 is a summary of the available elements in ANSYS program. The above table lists the element identification number, the name, the number of dimensions, the number of degrees of freedom per node, the number of nodes, and some features. ANSYS models are either two-dimensional or three-dimensional, depending upon the element types used. Two-dimensional models must be defined in the x-y plane and the nodes must be input using the two- dimensional format on the F cards. Three-dimensional models must be defined in the x-y-z plane and the nodes must be input using the three- dimensional formate on the F cards. The element input is included on the ANSYS program data input cards as shown in Table 5.2. The degrees of freedom associated with the model should be suffi- cient to characterize the actual response. Including unnecessary degrees of freedom or selecting elements with unnecessary features increases the solution core size and running time. The units of the element input and output parameters are described in Table 5.3 in terms of force (F), length (L), time (t), temperature (T), and heat (Q). Mass units can also be expressed as Ft 2 /L. 5.2 ELEMENT LIBRARY FOR STATIC ANALYSIS The three-dimensional isoparametric element (STIF45) and the three-dimensional interface element (STIF52) are recommended to use in a static analysis. 5.2.1 Three-dimensional Isoparametric Solid Element The three-dimensional isoparametric solid element is a higher- order version of the three-dimensional elastic solid element (STIF5). The higher-order element gives a considerable improvement of accuracy over the constant strain element. The advantage of isoparametric elements over constant strain elements is that, for a given accuracy, the number of degrees of freedom necessary to describe the structure may be reduced. Accordingly, not only the data preparation time, but also the computer wave- front solution time is reduced. The element has plasticity, but no creep or swelling capabilities. If all capabilities are needed, STIF49 should be used. The isoparametric solid element is defined by eight nodal points having three degrees of freedom at each node: translations in the nodal x, y , and z direction. An option is available to print out the stresses and strains on particular element surfaces when the surfaces are fr^e surfaces of the structure. Other options are available to print stresses at the inte- gration points or at the nodes. A summary of the isoparametric solid 60 element parameters is given in Table 5.4. Input Data . The geometry, nodal point locations, face numbers, loading, and the coordinate system for this family of elements are shown in Fig. 5.1. The element is defined by eight nodal points and the material properties. The nodal points should be numbered in the order shown in Fig. 5.1. The number of nodes input on Card El defines the type of solid element used. The material" may. be orthotropic, with ten elastic constants required for its specification. The three addi- tional shear modulus terms are optional and may be included for a more complete description of the material. If not included, the values are computed from the other input properties. There are no real constants required for this element. The element loading can be either temperature gradients (specified by nodal temperatures) or pressures (on one or more faces), or a combination of both. The data input for the isoparametric solid element is as follows: 1) only the eight node element with six pressure surfaces is available; 2) plasticity capability is included; 3) printout is available on a second surface for elastic solutions, as the numerical integration points, and at the nodal points; 4) the incompatible displacement modes may be suppressed with KEYSUB(IB), and 5) the number of number integra- tion points may be selected for elastic solutions with KEYSUB(IA). Output Data . The solution printout associated with the isopara- metric solid element is summarized in Table 5.5. Figure 5.2 shows a schematic STIF45 element output. Theory . The element formulation includes incompatible displacement modes. Either a 3x3x3 or a 2x2x2 lattice of integration points is available for use with the numerical (Gaussian) integration procedure. Assumptions and Restrictions . Zero volume elements are not allowed. Elements may be numbered either as shown in Fig. 5.1 or may have the planes IJKL and MNOP interchanged. Also, the element may not be twisted such that the element has two separate volumes. This occurs most fre- quently when the elements are not numbered properly. The dihedral angle between adjacent element faces should be less than 180°. All elements must have eight nodes. A "triangular" shaped element may be formed by defining duplicate K and L and duplicate and P node numbers. The extra mode shapes are automatically deleted for "triangular" shaped elements so that a "constant strain" element re- sults. The first two lines of the element solution printout are valid for both isotropic and orthotropic materials. The principal strains (line 3) are not valid for orthotropic materials. The principal stresses and the maximum shear stresses, however, are valid for orthotropic materials. 61 Surface stress outputs are valid only for isotropic elastic materials for which this face is a fr^e surface of the structure. Surface stresses should not be requested on the zero area face of "triangular" shaped elements. The 2x2x2 lattice of integration points is automatically used with plasticity solutions (K13 > on Card CI). 5.2.2 Three-dimensional Interface Element The three-dimensional interface element represents two parallel surfaces in space which may maintain or break physical contact and may slide relative to each other. The element is capable of supporting only compression in the direction normal to the surfaces and shear (Coulomb friction) in the tangential directions. The element has three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element may be initially pre-loaded in the normal direction or it may be given a gap specification. A specified stiffness acts in the normal and tangential directions when the gap is closed and not sliding. Because of the nonlinearity of the element an iterative solution procedure is required. A summary of the three-dimensional interface element parameters is given in Table 5.6. Input Data . The geometry, nodal point locations, and the coordi- nate system for the interface element are shown in Fig. 5.3. The element is defined by two nodal points, an interface stiffness, an initial gap (or interference, and an initial element status. The orientation of the interface plane (unlike STIF12) is defined by the nodal point locations. The plane is assumed to be perpendicular to the 1-0 line. The element coordinate system has its origin at node I and the x-axis is directed toward node J. The interface plane is parallel to the element y, z plane. The stiffness, k, may be computed from EA/L -- where the parameters are determined from the adjacent element. The effective length, L e «, is arbitrary, but may be on the order of 1/10 of the adjacent element length. The stiffness may also be computed from the maximum expected force divided by the maximum allowable surface displacement. In most cases k is several orders of magnitude greater than the other stiff- nesses in series with it so that its exact value is not critical. The initial gap (GAP) may be positive or negative. 'If negative, an ini- tial interference of this amount exists. The initial element status (START) is used to define the "previous" condition of the interface to be used at the start of the first iteration. This input overrides the condition implied by the gap specification and is useful in anti- cipating the final interface configuration and thereby reducing the number of iterations required for convergence. This parameter is also useful for inputting the element status in a run which is to be con- tinued, as determined from a previous ANSYS run. S2 The only material property required is the interface coefficient of friction, u. A zero value should be used for friction less surfaces. Temperatures (used if u is temperature dependent) may be specified at the element nodes. For some problems, a loss of contact or a sliding at the interface isolates a portion of the structural model not having sufficient displacement constraints. The KEYSUB(l) option, therefore, may be used to maintain a small force across and along the interface, maintaining stability while causing only a negligible inaccuracy in the analysis. The KEYSUB(2) option may be used whenever friction may cause some gap elements to oscillate slightly between a sliding and a stick- ing status. Output Data . The solution printout associated with the three- dimensional interface element is summarized in Table 5.7. The value USEP is the normal displacement (in the element x-di recti on) betw een the interface surfaces at the end of this iteration, that is, USEP = (u ), - (u )- + GAP. This value is used in determining the normal force. Note, the normal force will not be an equilibrium value unless this iteration represents a converged solution. The value USLIDE is the accumulated amount of surface sliding at the end of this iteration. Sliding may occur in both the element y and z coordinate directions. Note, sliding occurs in the iteration after the limiting tangential force is exceeded. KTYPE describes the status of the element at the end of this iteration for use in the next itera- tion. The surface may be in rigid contact (KTYPE=1), sliding contact (KTYPE=2), or frze (KTYPE=3). If, for example, KTYPE* 3 at the end of an iteration, an element stiffness of zero is used for the next itera- tion. The KTYPE values may be input *or START if a new run is to continue from this iteration. If no other effects are present ':nd KEYSUB(2)=0, convergence occurs whenever the gap status remains unchanged. For a friction! ess surface, the converged gap status is either KTYPE=2 or 3. Whenever KEYSUB(2) > 0, an element having sliding force oscillations within a defined tolerance range on u F , resulting in an oscillating gap status (KTYPE=1 , 2, etc.), is accepted as converged. This tolerance range is usually within the uncertainty range of u. Theory . The displacement functions for the interface element can be separated into the normal and tangential directions since they are basically independent. In the normal (element x) direction, when the normal force (F ) is negative, the interface remains in contact n and responds as a linear spring. As the normal force becomes positive, contact is broken and no force is transmitted (unless !<EYSUB(1 )=1 , then a small force is supplied to prevent a portion of the structure from being isolated). In the tangential directions, for F < and the absolute value of the tangential force (F ) less than or equal to (u F n ), the inter- face does not slide and responds as a "linear spring in the tangential 63 direction. However, for F„ < Q and F„ > u F„ , sliding occurs. Note n s r n that F„ is a variable and if contact fs broken, the tanaential function n degenerates to a zero slope straight line through the origin (or of slope K/1Q\ if KEYSUB(IH) indicating that no Cor little) tangential force is required to produce sliding. Figure 5,4 shows the displace- ment functions for this element. Assumptions and Restrictions . The gap size may be specified independently of the nodal point locations. Nodes I and J, however, may not be coincident since the nodal locations define the interface plane orientation. The element is defined such that a positive normal displacement (in the element coordinate system) of node J relative to node I tends to open the gap. Recall that the element coordinate system is defined by the I and J node locations. The nodes defining the element may have arbitrarily rotated nodal coordinate systems since a displacement transformation into the element coordinate system is included. The friction coefficient may be input as a function of temperature and is evaluated at the average of the two node temperatures. For this nonlinear element an iterative solution procedure is required with the stiffness matrix re- formulation each iteration. Note, the effect of the element status changed in this iteration does not appear until the next iteration. Non-converged solutions are not in equilibrium. If GAP=0.Q (or blank), the element stiffness is included in the first iteration, unless START=3.0. The element operates only in the Static (K2O0) and the Nonlinear Transient Dynamic (K2Q=4) analyses. If used in other analysis types, the element maintains its initial status throughout the analysis. Note, a gap condition capability is also included in the Reduced Linear Transient Dynamic (K20=5) analysis. The element coordinate system orientation angles a and 8 (shown in Fig. 5.3) are computed by the program from the nodal point locations, a ranges from 0° to 360° and S from -90° to +90°. Elements lying along the +Z axis are assigned values of a=0°, S= + 90°, respectively. The element coordinate system for a=0°, 8=90° is shown in Fig. 5.3. Elements lying off the Z-axis have their coordinate system oriented as shown for the general a, 2 position. Note, for a=90°, 3^90°, the element coordinate system flips 90° at the Z-axis. 5.3 ELEMENT LIBRARY FOR HEAT TRANSFER For a heat transfer analysis, it is recommended to use the iso- parametric quadrilateral temperature element (STIF55) and the two- dimensional conducting bar (STIF32). 5.3.1 Isoparametric Quadrilateral Temperature Element The isoparametric quadrilateral temperature element can be used as a biaxial plane element or as an axisymmetric ring element with a two-dimensional thermal conduction capability. The element has four 64 nodal points with a single degree of freedom, temperature, at each node. The isoparametric temperature element. is a higher-order version of the two-dimensional linear temperature element (STIF35). The advantage of isoparametric temperature elements over linear temperature elements is that, for a given accuracy, the number of degrees of freedom necessary to describe the structure may be reduced. Accordingly, the data pre- paration time and the computer wave front solution time are also reduced. The isoparametric temperature element is applicable to a two- dimensional, steady-state or transient, Thermal (K20=-l) analysis. If the model containing the isoparametric temperature element is also to be analyzed structurally, the element should be replaced by an equiva- lent structural element. The nodal temperatures determined from the isoparametric temperature element are applied to the corresponding structural nodal points. A summary of the isoparametric quadrilateral temperature element parameters is given in Table 5.8. Input Data . The geometry, nodal point location, face numbers, loading and the coordinate system for the isoparametric temperature element are shown in Fig. 5.5 The isoparametric temperature element must have four nodes. The thermal conductivities are defined in the global X and Y directions. The specific heat and the density may be assigned any values for steady-state solutions. An average internal heat generation rate may be applied to the element. All of the element lateral surfaces have convection capability and are numbered as shown in Fig. 5.5. Output Data . The solution printout associated with the isopara- metric tamperature element is as shown in Table 5.9. Theory . The theory on which the isoparametric temperature element is based as described for the STIF35 element, except for the tempera- ture function. The temperature function in this element is not a linear polynomial, but includes additional incompatible temperature modes. A 3x3 lattice of integration points is used for the numerical (Gaussian) integration procedure. Assumptions and Restrictions . The isoparametric quadrilateral temperature element must not have a negative or a zero area. The element must lie in an X-Y plane and the X-axis must be the radial direction for axi symmetric problems. Also, axi symmetric structures should be modeled in the +X quadrants. A triangular elememt may be formed by defining duplicate K and L node numbers. The extra mode shapes are automatically deleted for tri- angular elements so that a linear temperature element results. Face 3 should not be defined as a convection surface if nodes K and L are coincident. If the thermal element is to be replaced by an analogous structural element with surface stresses requested, the thermal element should be oriented such that face 1 and/or face 3 is a free surface. 65 5.3.2 Two-dimensional Conducting Bar The two-dimensional conducting bar is a uniaxial element with the ability to conduct heat between its nodal points. The element has a single degree of freedom, temperature, at each node point. The con- ducting bar is applicable to a two-dimensional (plane or axi symmetric) steady-state or transient Thermal (K20=-l ) analysis. If the model containing the conducting bar element is also to be analyzed structurally, the bar element should be replaced by an equiva- lent structural element. The node temperatures determined from the conducting bar element are applied to the corresponding structural element's nodal points. Structural elements accepting a transverse temperature gradient are given a uniform temperature in that direction by averaging the nodal temperatures. A summary of the two-dimensional conducting bar element parameters is given, in Table 5.10. Input Data . The geometry, nodal point locations, loading, and coordinate system for the conducting bar element are shown in Fig. 5.6. The element is defined by two nodal points, a cross-sectional area, and the material properties. Note that for an axi symmetric analysis, the area must be defined on a "per radian" basis. The specific heat and the density may be assigned any values for steady state solutions. The thermal conductivity is in the element longitudinal direction. An average internal heat generation rate may be applied to the element. Output Data . The solution printout associated with the conducting bar element consists of the node temperatures, T(I) and T(J), which are included in the overall nodal temperature solution printout. Theory . The temperature distribution for this element is obtained from the numerical- solution of the following equation: where K s thermal conductivity (Heat/Length*Time*Deg) p = density (Weight (or Mass)/Volume) C = specific heat (Heat/Weight (or Mass)*0eg) q ■ internal heat generation rate (Heat/Volume*Time) The temperature function is a, linear polynomial of the form: T(x) = C-J + C 2 x where the x-axis extends from node I to node J. Assumptions and Restrictions . Heat is assumed to flow only in the longitudinal element direction. The element must be in an X-Y plane and the global X-axis must be the radial direction for axi symmetric problems. The element must not have a zero length, so nodes I and J must not be coincident. 66 5.4 ELEMENT LIBRARY FOR THERMAL STRESS ANALYSIS It is recommended to use the two-dimensional isoparametric element (STIF42) and the two-dimensional interface element (STIF12) in a thermal stress analysis. 5.4.1 Two-dimensional Isoparametric Element The two-dimensional isoparametric element is a higher-order version of the two-dimensional constant strain element (STIF2). The higher- order element gives a considerable improvement of accuracy over the constant strain element. The advantage of more complex elements over constant strain elements is that, for a given accuracy, the number of degrees of freedom necessary to describe the structure may be reduced. Accordingly, the data preparation time and the computer wave- front solution time is also reduced. The element has plasticity, but no creep or swelling capabilities. If all capabilities are needed, STIF2 should be used. The isoparametric element is defined by four nodal points having two degrees of freedom at each node: translations in the nodal x and y directions. The element may be used as a biaxial plane element or as an axisymmetric ring element. An option is available to print out the stresses and strains on particular surfaces of the element when the surfaces are free surfaces of the structure. .Other options are available to print stresses at the integration points or at the nodes. A summary of the two-dimensional isoparametric element parameters is given in Table 5.11 . Input Data . The geometry, nodal point locations, face numbers, loading, and the coordinate system for this element are shown in Fig. 5.7. The element input data includes four nodal points, a thickness (for a plane stress option only) and the orthotropic material proper- ties. The element loading may be input as any combination of node temperatures, node fluences, and element pressures. The nodal forces should be input per unit of depth for a plane analysis (except for KEYSUBO ) s 3) and per radian for an axisymmetric analysis. The data input for the isoparametric element is as follows: 1) only the four-node element with four pressure surfaces is available; 2) creep and swelling capabilities are not included; 3) printout is avaiable on a second free surface for elastic solutions, at the numeri- cal integration points and at the nodal points; and 4) the incompatible displacement modes may be suppressed. Output Data . The solution printout associated with the two- dimensional isoparametric element is summarized in Table 5.12. Line K-L is analogous to line I -J except that it applies to the opposite surface. Figure 5.8 shows a schematic STIF42 element output. Theory . The element formulation includes incompatible displace- ment modes. A 3x3 lattice of integration points is used with the numerical (Gaussian) integration procedure. 67 Assumptions and Restrictions . The area of the element must be positive. Zero area elements will print out an error message and con- tribute nothing to the total stiffness. Negative area elements print out a warning message and will not plot correctly. The numbering of the nodes should be counter-clockwise in the coordinate system shown in Fig. 5.7. The two-dimensional isoparametric element must lie in an X-Y plane and the global X-axis must be the radial direction for axi symmetric problems. An axi symmetric structure should be modeled in the +X quadrants, A triangular element may be formed by defining duplicate K and L node numbers. The extra mode shapes are automatically deleted for triangular elements so that a constant strain element results. The surface stress printout is valid only for isotropic, elastic elements for which this face is a fr^e surface. Surface strains, however, are valid for both isotropic and orthotopic elements. Surface stress printout on an X=0 face of axi symmetric elements or on the zero length side of a triangular element should not be requested. 5.4.2 Two-dimensional Interface Element The two-dimensional interface element represents two plane or axisymmetric surfaces which may maintain or break physical contact and may slide relative to each other. The element is capable of supporting only compression in the direction in the normal to the surfaces and shear (Coulomb friction) in the tangential direction. The element has two degrees of freedom at each node:, translations in the nodal x and y directions. The element may be initially pre-loaded in the normal direction or it may be given a gap specification. A uniform stiffness acts in the normal and tangential directions. Because of the overall nonlinearity of the element an iterative solution procedure is required. A summary of the two-dimensional interface element parameters is given in Table 5.13. Input Data . The geometry, nodal point locations, and the coordi- nate system for the interface element are shown in Fig. 5.9. The element is defined by two nodal points, an angle to define the inter- face plane, a stiffness, an initial displacement interference, and an initial element status. The stiffness, if left eq ual to zero, defaults to 10 s . An element coordinate system (x-y) is defined on the inter- face plane. The angle 9 is input in degrees and is measured from the global X axis to the element-x axis. Note, the orientation of the interface plane is defined by. the angle 9 and not by the nodal point locations. The stiffness, k, may be estimated from EA/L -- where the para- meters are determined from the adjacent element. The effective length, L-xra is arbitrary, but may be on the order of 1/10 of the adjacent element length. The stiffness may also be computed from the maximum expected force divided by the maximum allowable surface displacement. In most cases k is several orders of magnitude greater than the other 68 stiffnesses in series with it so that its exact value is not critical. The stiffness should be "per radian" for an axt symmetric analysis. The initial displacement interference, 6, defines the displacement interference (if positive) or the gap size (.if negative). The Initial element status (START) is used to define the "previous" condition of the interface to be used at the start of the first iteration. This input is used to override the condition implied by the interference specification and is useful in anticipating the final interface confi- guration and reducing the number of iterations required for convergence. This procedure may also be used to continue a previous analysis . The on.ly material property required is the interface coefficient of friction, u. A zero, value should be used for friction less surfaces. Temperatures may be specified at the element nodes. For some problems, a loss of contact or a sliding at the interface isolates a portion of the structural model not having sufficient displacement constraints. The KEYSUB(l) option may be used to maintain a small force across and along the interface, maintaining stability while causing a negligible inaccuracy in the analysis. The K£YSUB(2)=1 option should be used whenever friction is present and there is the possibility of some gap elements oscillating slightly between a sliding-sticking status. Output Data . The solution, printout associated with the two- dimensional interface element is summarized in Table 5.14. The value USEP is the normal displacement between the interface surfaces at the end of this iteration, that is: USEP = (u ) , - (u w ) T - <3 y « y i This value is used in determining the normal force. For an axi symmetric analysis, the element forces are expressed per radian of circumference. The value USLIDE is the accumulated amount of surface sliding at the end of this iteration. KTYPE describes the status of the element at the end of this itera- tion. It KTYPE=1 , the gap is closed and no sliding occurs. If KTYPE=3, the gap is open. If at the end of an iteration KTYPE=3, an element stiffness of zero is used for the next iteration. A value of KTYPE=+2 indicates that node J moves to the right of node I as shown in Fig. 5.9. KTYPE=-2 indicates a negative slide. If no other effects are present and KEYSUB(2)=0, convergence occurs whenever the element status remains unchanged. For a frictionless surface (u=0.0), the converged element status is either KTYPE=+2 or 3. Wherever KEYSUB(2) > 0, an element having sliding force oscillations within a defined tolerance on U F , resulting in an oscillating element status (KTYPE=1, 2, etc.), is accepted as converged. This tolerance range is usually within the uncertainty range of u. Theory . The displacement functions for the interface element can be separated into the normal and tangential directions because they are basically independent. In the normal direction, when the normal force (F ) is negative, the interface remains in contact and responds as a linear spring. As 59 the normal force becomes positive, contact is broken and no force is transmitted (unless KEYSUB(1 )*1 , then a small force is supplied to prevent a portion of the structure from being isolated). In the tangential direction, for F < Q and the absolute value of the tangential force (F ) less than or equal to (u F ), the interface x y does not slide and responds as a linear spring in the tangential direc- tion. However, for F < and F > u F , sliding occurs . Note that y x y F v is a variable and if contact is broken, the tangential function A degenerates to a zero slope straight line through the origin (or of slope k/10 5 , if KEYSUBOH ) indicating that no (or little) tangential force is required to produce sliding. Figure 5.10 shows the displace- ment functions for this element. Assumptions and Restrictions . The gap interference is specified independent of the nodal point locations. Nodes I and J may be coin- cident since the orientation of the interface plane is defined only by the angle 8. The element is defined such that a positive normal dis- placement (in the element coordinate system) of node J relative to node I tends to open the gap, as shown in Fig. 5.9. If, for a given set of conditions, nodes I and J are interchanged, or if the interface is rotated 8 + 180°, the gap element appears to act as a hook element, i.e., the gap closes as the nodes separata. The element may have rotated nodal coordinates since a displacement transformation into the element coordinate system is included. The friction coefficient is evaluated at the average of the two node temperatures. The two-dimensional interface element must be de- fined in an X-Y plane and the global X axis must be the radial direc- tion for axi symmetric problems. The element operates only in the Static (K20=0) and the Nonlinear Transient Dynamic (K20=4) analyses. If used in other analysis types, the element maintains its initial status throughout the analysis. Note, a gap condition capability is also included in the Reduced Linear Transient Dynamic (K20=5) Analysis. No moment effects are included due to nodal points offset from a line perpendicular to the interface. If INTERFERENCE is zero (or blank), the element stiffness is included in the first iteration, un- less START = 3.0. The element requires an iterative solution with the stiffness matrix reformulated each iteration. Note that if the element status changes within an iteration, the effect of the changed status is included in the neat iteration non-converged iterations are not in equilibrium. 70 TABLE 5.1 ELEMENT SUMMARY 7A3LE STIfFMgSS NO. NAHg 6 a 9 10 1 1 12 13 u 13 16 17 la 19 20 21 22 23 2* 25 26 27 23 29 30 31 32 23 34 35 36 37 33 39 ^0 3?AP, 2-0 CONSTANT STRAIN .ELEH . EL-ST'C 3EAM-, 2-3 ELASTIC 5EAM-. 3-3 ELASTIC SOLID (C3T) SLAS- "LA7 TRI. PLATE S?AR» 3-0 ELASTIC STRAIGHT PIPE CA3LE AXlSYM. CONICAL SMELL INTERFACE ElEM. (2-01 EL if- FLAT TPT. SMELL S?RING-DAMP£R MASS WITH PqTaRY INER. MASS* 2-0 MASS* 3-0 SPRING* 2-0 OAMPEP » 2-0 PLASTIC STRAIGHT PIPE GENERAL M^ss COPE SPACED ANO GAP PLASTIC 3EAM-, 2-0 TOPS ION 5PRING-0A.MPEP AXIS?*. HARMONIC QUAD. PLAS. FLAT 7RI. PLATE STIFF, DAMP, "A55 MATRIX PL FLAT SMELL (3 TEMP) CURVED PIPE (EL30VO CONDUCTING SOLID RADIATION LINK CONDUCTING 3AR, 2-0 CONDUCTING pap, 3-0 CONVECTION L INK LINEAR TEMPER. EL. NOUCTANCE >ci I HYO° iULlC CONQUC'I^G FLAT SH; FLUID COUPLING SLIDING INTERFACE COM3 InaT ION ELEVEN - OIH. 2 I 2 3 3 2 3 3 3 2 2 3 2>3 2 2 3 2 ? 3 2>3 2 2 3 2 2 3 3 3 3 2 OH 2 3 2 OR 2 OP 3 OR OP OR OOF NODES TYPE 2 3»A 2 2 A-»6»3 3 2 2 2 2 2 3 2 1 1 1 2 2 2 1 2 2 2 A 3 2 3 3 At 6 »-3 2 2 2 2 3*4 2 3 2 2 2 PLASTIC PLASTIC LINEAR LINEAR LINEAR LINEAR PLASTIC LINEAR NON-LIN LINEAR NON-LIN LINEAR LINEAR LINEAR LINEAR LINEAR LINEAR LINEAR PLASTIC LINEAR NON-LIN PLASTIC LINEAR LINEAR PLASTIC LINEAR PLASTIC LINEAR LINEAR NON-LIN LINEAR LINEAR LINEAR LINEAR NON-LIN LINEAR LINEAR NO N -LIN NON-LIN USE STIF21 USE USE USE USE STIF21 3TIF21 5TIF1A STIFIA USE STIF14 USE STIFiQ (CONTINUED ON NEXT PAGE) 71 "A8LE I (CONTINUED) ST IF r nESS MO- NAME OI». DOF NOOES TYPE 4i 3—3 ELAS..CUAO. MEMS. 42 LINEAR STRAIN I3QPAP. 43 EL AS- FLAT PECT. SHELL 4-A, TiPEPED UNSYM.. SEAM 43 ISOPARAMETRIC SOLID 46 ELAS. PLAT PECT. PLATE 47 TSANSV.HT.CCNO. SHELL 2 43 PL. PLAT SHELL !S TEH?) 49 PLASTIC SOLID 50 SU?EP-EL£H£NT 32 INTERFACE ELS*. (3-0) 53 LAMINATED 5HELL 54,. TAPER. UNSYM. SEAM (2-0) 53 ISCPAP.QUAO.TEHP.ELEM 56 FLUID FL-HT TRANS PIPE 57 ISO. QUAD. SHELL TEMP. 53 PLASTIC HINGE ELEM. 59 IMMERSED PIPE ELEM. 60 PLASTIC EL50W 61 A^IS7H. HARMONIC SHELL 62 2-0 WAVE ELEMENT 63 ELAS. "LaT CUaO. SHELL 65 3-0 *AYE ELEMENT 66 TPANS. THEPM-fLOW PIPE 67 HT TPANS-ELECTPIC CUAO 63 HT TPANS-ELECTPIC LINE 69 HT TPAN-ELECTPIC SOLID 70 ISO, CONOUCTING SOLID 71 LUMPED 7HEPMA>_ MASS 2 73 AXISY HARMONIC TEMP EL 3 3 4 LINEAR 2 2 4 PLASTIC 3 6 4 LINEAR 3 6 3 LINEAR 3 3 3 PLASTIC 2 3 4 LINEAR OP 2 1 5 LINEAR 3 6 3 PLASTIC 3 3 4.6.3 PLASTIC 3 • - LINEAR 3 3 2 NON-LIN 3 6 3 LINEAR 2 3 2 LINEAR 2 I 4 LINEAR 3 2 2 NON-LIN 3 1 4 LINEAR 3 6 2 NON-LIN 3 6 2 LINEAR 3 6 3 PLASTIC 2 4 2 LINEAR 2 2 4 LINEAR 3 6 4 LINEAR 3 2 3 LINEAR 3 2 2 NON-LIN 2 2 4 ITERATIVE 3 2 2 ITERATIVE 3 2 3 ITERATIVE 3 1 3 LINEAR CP 3 1 1 LINEAR 2 1 4 LINEAR 72 Table 5.2. Input of Element Parameters on ANSYS Program Data Cards Input Element- Parameter on Card NODS NUMBERS El REAL CONSTANTS 02 or E2 TEMPERATURES, FLUENCES Q. •PRESSURES P HEAT GENERATION RATES a CONVECTION SURFACES P MATERIAL PROPERTY EQUATIONS H KEYSU8(N) Table 5.3. Units of Input and Output Parameters Input Parameter Un i ts Area L 2 Volume \? Pressure F/L Moment of Inertia L Fluence (?t) Neutrons/L Density M/l 3 Convection Coefficient Q/L -t-T Conduct i vi ty Q/L-t-T Specific Heat Q/M-T Heat Generation Rate Q/l -t (except for STIF71 ) (Q/t) Spring Constant F/L Damping Coefficient F-t/L 2 Rotational Inertia F-^-t 2 Output Parameters Units Stress F/L 2 Strain Moment or Torque L-F Twist Radians Heat Flow Rate Q/t 74 TA3LE 5.4. ISOPARAMETRIC SOLID ELEMENT - THREE IMENSIONAL SUSPOUTINE NAM£ NO. C. c NODES PER ELEMENT DEGREES Or FacZOQH ?€5? NOCE R£<3UTfi£0 RE-L CONSTANTS TEMPERATURES PRESSURES MATERIAL PROPERTY EOUATIONS MATRTCES CALCULATED PLASTICITY CREEP ANO SWELLING FORCES SAVED ON TAPE KEYSU3U) KEYSuS(lA) KEYSU3(13> STIFFS a 3 3 6 I»J»KtL»M,N»0»P UX.UYtUZ 10 TCI) »T(J) ,T<K) ,T(L) »T(H) ,7(N) » T(O) ,T(P) P(IJXL) jP (IJNM) ,P(JKON) ,?(KLPO) , P(LIMP) »P(NHCP) EX ♦ EY , EZ y ALPX » ALPY , Al_PZ > NUXY ,NUTZ >NUXZ » OENS . GXY*GYZ>GXZ (OPTIONAL) HASSt STIFFNESS YES NO - GENERAL 3-0 APPLICATION 1 - GENERALIZED PLANE STRAIN OPTION - USE 3X3X3 LATTICE CF INTEGRATION POIN (USED FOR INCREASED ACCURACY WITH WARPED ELEMENTS ANO ELEMENTS HAVING HIGHLY NON-RECTANGULAR SHAPES) 1 - USE 2X2X2 LATTICE OF INTEGRATION POIN (KEYSUS(IA) IS INTERNALLY SET TO 1 F PLASTICITY SOLUTIONS) - DISPLACEMENT FORMULATION INCLUDES Th.E EXTRA HOOE SHAPES 1 - DISPLACEMENT FORMULATION OOES NOT INCLUDE THE EXTRA MODE 5HAPE5 (CONTINUED ON NEXT PAGE) 75 TA8LE 5.4 (CONTINUED) XEYSU3(2) C - NO SURFACE STRESS OUTPUT 1 - PRINT GUT STRESSES FOR SURFACE 2 2 - PRINT GUT STRESSES FOR 5GTK SURFACES 2 AiNO ; (SURFACE STRESSES AVAILABLE FOR ISOTROPIC, ELASTIC MATERIALS ONLY) 3 - PRINT GUT SOLUTION AT EACH INTEGRATION POINT AS WELL AS AT CSNTROIO (FOR PLASTICI7C SOLUTIONS ONLY. NOTE - AOOS 21 MORE LIMES ? c 3 SLZ&EIT) 3 - PRINT STRESSES AT THE 3 NODES AS WELL AS AT CSNTROID SUBROUTINE GATE V 30/72 X V I T * XXXXXXXXX ** 9' M X M . T M ■ ? W W X ' J F X » ■ • M ^t f H^I A M A A A A * A A ■ ' X ' J J TT » W J f M. X X - ■ M 76 TABLE 3.5 ISOPARAMETRIC SOLID ELEMENT - THREE OIMSNSIONAL EL£M£?*T PRINTOUT EXPLANATIONS EXPLANATION LAoEL NUMBS?. C3NSTA^ 0? ITS FOP MAT LINE 1 SQL in NOOSS xc»rc»2C TEMP 1 a 3 1 15 ais 3F3.3 F5.0 LINE 2 EPS 6 6F9.6 SIG 6 6F3.<3 LINE 3 SIGPo TAUMaX EP?R VOL VM 3 i 3 1 1 3F3.0 F7.0 3F9.6 F12.3 F3.0 ELEMENT NUMBER MOOES I>J->K,L»H,N,0»P X,Y,Z COORD I?JAT£3 OF ELEMENT CcNTROID ELEMENT AVERAGE TEMPERATURE E?X»E?Y,E?Z>GAMMAXY»GAMMAYZ»GAHMAX2 (GLOBAL (ELASTIC STRAIN COMPONENTS) SIGX»SIGY»5IGZ>TAUXY>7AUYZ>TAUXZ (GLOBAL J PRINCIPAL STRESSES SIG1 ,S IG2 >SIGD MAXIMUM S'ritM^ STRESS PRINCIPAL STRAINS ER1 , E?2 . E?3 (ISOTRCP-IC ELEMENT VOLUME VON MI3ES EOUIVALENT STRESS LINE IJNM SURFACE 2 STRESS CONDITIONS (PRINTED ONLY IF x£YSUS<2) IS GREATSp THAN ZERO) SURFACE AREA AVERAGE SURFACE TEMPERATURE SIGX» SIGYt AND TAUXY (X AXIS PARALLEL TO TM£ AVERAGE Or LINES I- J ANO M-N) VMS 1 F3.0 VON MISES EOUIVALENT STRESS FOR THIS FACE LINE IJNM SURFACE 2 STRESS CONDITIONS (CONTINUED) MAXIMUM* MINUMUM* ANO MAXIMUM SMEaR STRESS ON SURFACE 2 OF THIS ELEMENT ANGLE OF PRINCIPAL STRESSES (MEASURED FROM LOCAL X TOWAflO LOCAL Y) EPSX. E?SY, ANO GAMMAAY SURFACE PRESSURE (CONTINUED ON NEXT PAGE) AREA 1 F10.A TEMP 1 F<9.0 XY STR 3 3F3.0 HAX-MlN STR 3 3F3.0 A 1 F5.1 STRAINS PRESSURE 3 1 3F9.Q ~ Fa.o 77 TA6LE 5.5 (CONTINUED) LINES KL?0 SURFACE <* STRESS CONDITIONS (PRINTED ONLY IF" *SYSUS(2) = 2) (SAME AS SURFACE 2 OUTPUT 3UT APPLIED To SURFACE <*> LINES 4 ANO 5 NONH-INEAS SOLUTION (PRINTED ONLY IF K13 IS GREATER THAN ZERO ON CAPO CD SRPLAV 6 6F10.7 AVERAGE PLASTIC STRAINS AT CENTROIO (X*Y,Z»XY,YZ>*Z) SPORiV 6 6F10.7 AVERAGE ORIGIN SHIFT STRAINS AT CENTROIO' LINE 6 NON-LINEAR SOLUTION (CONTINUED) EPGNAV I FI0.7 AVERAGE GENERALIZED STRAIN AT CENTROIO ROSGAV 1 F1Q.4 AVERAGE GENERALIZED POISSONS RATIO AT CENTROIO SIGEiV 1 F10.2 AVERAGE EQUIVALENT STRESS AT CENTROIO NOTE - STRESSES ANO STRAINS ARE PRINTED A?TER THE PLASTICITY CORRECTIONS. 78 TABLE 5.3 INTERFACE ELEMENT - T iREE-OIMENSlCNAL SUBROUTINE NAME STIF3E NO. Or NODES PER ELEMENT 2 I>o 0EGPEE"S OF FREEDOM P*R NOOE 3 UX»UY»UZ REQUIRED SEAL CONSTANTS 3 STIFFNESS >GAP , START A NEGATIVE GAP ASSUMES A.N INITIAL INTERFERENCE CONDITION IF START = 0.0 OP BLANK, PREVIOUS STA OF ELEMENT DETERMINED FROM GAP INPUT IF STAPT = l.Ot GAP PREVIOUSLY CLOSED . AND NOT SLIDING IF STAPT =2.0* GAP PREVIOUSLY CLOSED AND SLIDING IF STAPT * 3.0* GAP PREVIOUSLY OPEN TEMPERATURES Z T(I)»T(J) PPESSijRES MATERIAL PROPERTY EQUATIONS 1 HU MATRICES CALCULATED STIFFNESS PLA-5TICITY NO NON-'-INE-R YES (ITERATIVE SoL'JTIcn REQUIRED) FORCES SAVED ON TAPE 2 NORMAL FORCE (FN )» TANGENTIAL FGPCE(FS) KEYSUB(l) - NO STIFFNESS ASSOCIATED WITH SEPARATED INTERFACE 1 - STIFFNESS»1.0E-6 ASSOCIATED WITH SEPARATED INTERFACE FOR NORMAL MOTION ANO WITH SLIOING INTERFACE FOR TANGENTIAL MOTION XEYSUP<2) - CONVERGENCE BASED ON UNCHANGING GAP STATU 1 - CONVERGENCE 3ASED ON CHANGING GAP STATUS WITHIN A 5 PERCENT UNCERTAINTY ON MU" 2 - CONVERGENCE BASED ON CHANGING GAP STATUS WITHIN A 10 PERCENT UNCERTAINTY CN VU SUBROUTINE OATE 5/30/7D 79 TA3LE 5.7 INTERFACE ELEMENT - THREE-DIMENSIONAL ELEMENT PP1N7CUT EXPLANATIONS NUM9EP OF LASEL CONSTANTS FORMAT EXPLANATION LINE i 3-0 GiP 1 15 ELEMENT NUHSSP H03£5 2 2 IS NODES I AND J USE?»USLICECY,Z) 2 2F9.3 GAP SIZE. SLIDING CISTA.NCE IN LOCAL QIRECTTON» SLIDING DISTANCE IN L'OC Z OIRECTION KTY?5 1 12 INTERFACE CONDITION INOICATOP 1 - RIGID CONTACT 2 - SLIDING CONTACT 3 - FREE KOLD 1 12 XTYPE VALUE OF THE PREVIOUS ITEPATIC LINE" ? FN 1 G14.6 NORMAL FORCE (ALCNo I-J LIME) F3 1 G14.6 TANGENTIAL FORCE (VECTOP SUM) 80 TABLE s.3 ISOPARAMETRIC QUAOPILATEPAL TEMPERATURE ELEMENT SU3P0UTINE NAME STIF35 NO. Or MOOES PEP ELEMENT - I»J»K,L DECREES GF FREEDOM PEP MOOS 1 TEMP REQUIRED REAfc CONSTANTS HEAT GENERATION RATES 1 AVERAGE CONVECTION SUP?" ACES ^ lJ»UX,.<L»Ll HA7E.PIAL PROPERTY ECUA7I0NS ^ XXX»KYY »OENS»C CGLC8AL) MATRICES CALCULATED CONDUCTIVITY, SPECIFIC HEAT KEYSU3<1> - PLANE 1 - AXISYMMETPIC «EYSu3(lA) - INCLUDE EXT* A 7EHPEPA7URS SHAPES 1 - SUPPRESS E~7RA TEMPERATURE SHAPES KEYSUS(2: - NO CONVECTION SURFACE PRINTOUT 1 - PRINT OUT HEAT FLOW SATE FRO* CONVECTION SURFACES SVJSPOUTINE 0A7E 6/22/73 7A8LE 5.9 ISOPARAMETRIC GUACRILATERAL TEMPERATURE ELEMENT ELEMENT PRINTOUT EXPLANATIONS NUMBER OF LABEL CONSTANTS FORMAT EXPLANATION LINE i _ (PRINTED ONLY IF K£YSUS-(2) = 1) ELEMENT NUMBER CONVECTION FACE NOOES (I»J OR J*K OR ,K,L OR L»I) CONVECTION -ACE NUMBER CONVECTION SURFACE AREA AVERAGE FACE TEMP, FLUID SULK TEMP. HEAT FLOW RATE ACROSS FACE LINES 2>2»- (SAME AS ABOVE FOR OTHER CONVECTION SURFACES* IF DEFINED) ELEMENT NOOES 1 2 15 2IS FACE AREA 12 Fa.* TAVG.T3ULX HEAT FLOW 2 1 2F6.0 Gil. A 81 TABLE 5.10 CONDUCTING BAR - TWO-DIMENSIONAL SUBROUTINE NAME NO. OF NODES PER ELEMENT DEGPEES OF FREEDOM PER NODE REQUIRED REAL CONSTANTS HEAT GENERATION ,RATES CONVECTION SURFACES MATERIAL PROPERTY EQUATIONS •MATRICES CALCULATED ELEMENT PRINTOUT SUBROUTINE OATE ST IF32 2 I,J 1 TEMP 1 AREA 1 AVERAGE 3 KXX.DENS.C CONDUCTIVITY .SPECIFIC HEAT NONE 7/' 01/70 p M x M' 'A' 'X X' 'X 'Jfc *X J 82 TABLE 5.11 TViO— DIMENSIONAL ISGPaflAHETRlC ELEMENT SUBROUTINE NAM? NO. OF NODES PES ELEMENT DEGREES 05" FREEDOM PER N02E REQUIRED PEAL CONSTANTS TENPFPATUnES PRESSURES MATERIAL PROPERTY EQUATIONS MATRICES CALCULATED PLASTICITY CREEP AND SWELLING FORCES SAVED CN TAPE KEYSua CD KETSuBClAJ STIFLE 2 1 6 10 I»J*X»L (NUMBER CCUNTER-CLQCXylSE) UX*UY IF" KSYSUS(l) = 0.1.2 THlCXNESS, IF XSYSU3U) » 3 Til) ,TU> ,T(X) »T(L) PCI) »P<2> *P<3) »P-(*) IF PLANE STRESS - EX ,SY .NUXY , AL?X , AL?Y ,OENS GXY (OPTIONAL) IF AXISYM OR PLANE STRAIN - EX,EY»E2,.NUXY,NUY2.NUX2»AL?X,ALPY> ALP2»0ENS GXY (OPTICNAL) MASS ♦STIFFNESS YES NO 26 SIGMAX.SlGMIN.TAUMAX.SIG2.SIGc. E?GSN»SIGX.S I GY,TAUXY. TEMPERATURE. W ELASTIC STRAINS, \ PLASTIC STRAI 4 0. SHIFT STRAINS, 4 THERMaL STRaI - PLANE STRESS 1 - AXISYHMETRIC 2 - PLANE STRAIN (2 STRAIN = 0.0) 3 - PLASZ STRESS WITH THICKNESS INPUT - DISPLACEMENT FORMULATION INCLUDES THE EXTRA MOOE SHAPES 1 - DISPLACEMENT FORMULATION DOES NOT INCLUOE THE EXTRA MOOE SHAPES (CONTINUED ON NEXT PAGE) 83 TABLE 5. IT (CONTINUED) <£YSuS(2} 3 - t+ - NO SURFACE STRE33 PRINTOUT PRINT OUT STRESSES FOR SURFACE I -J PRINT OUT STRESSES FOR 30TH SURFACES I -J AND K-L (SURFACE STRE33 PRINTOUT AVAILABLE ONLY FOR ISOTROPIC. ELASTIC MATERIALS) PRINT OUT SOLUTION AT ALL INTEGRATION POINTS AS WELL AS AT CZNTROID (FOR PLASTIC SOLUTIONS ONLY. ADOS 15 MORE LINES ?Z? ELEMENT") PRINT STRESSES AT Th£ <+ NODES AS WELL AS AT CSNTROID (KEYSU8QA) MUST = 0) *£T5u3(2A) - PRINT SOLUTION A7 ELE.ME.NT CcNTROlD 1 - REPEAT LINES 1 ANO 2 OF SOLUTION FOR ALL OTHER INTEGRATION POINTS (ACOS 16 MORE LIN -13 PZri ELEMENT 1 SUBROUTINE OATE. ^/DO/72 34 TAfcLE 3.12 t'wo-oi^ensicnal isoparametric et.shs.nj element printout explanations LAS£L NUHSE.R OF CONS 7 AN 7 3 FORMA 7 line i EL EM NODES vol MA7EP I A STRESS S 1 3 E.~F L IM" 1 4^ i 1 1 I 15 415 "1 .A. 12 "3.0 F3.0 LINE 2 X Y i XY 3TR I 1 1 4. F6.2 F6.2 F5.0 4F 3 • 0- H.A^-T-»I*N 1 S7 R 3 3F3.0 A 1 F5.1 EXPLANATION ELEMENT NUM5SR N00S3 I* J, X, A.NO L VOLUME Of ELEMENT MATERIAL NUM9ER STRESS INTENSITY IN THIS ELEMENT VON MIScS EQUIVALENT STRESS X. COORDINATE C? CENTROID OF ELEMENT Y C00R0INA7E Or CENTpOID OF ELEMENT AVERAGE 7EHPERA-uRE OF ELEMENT SIGx, SIGY, TAUxY. -NO SIGZ (SIG2=0.0 FOR PLANE STPE3S ELEMENTS) 3IGHAX, SIGN IN, ANO TAUMAX (IN-PLANE PRINCIPAL STR£SS£3) ANGLE OF PRINCIPAL STRESSES RESTIVE TO 7h£ GL03AL X-Y ±ZZ5 LINE I -J SURFACE I -J STRESS CONDITIONS (PRINTED ONLY. IF KEYSU3<2> IS 1 OR 2) AVERAGE TEMPERATURE OF I-J SURFACE ELASTIC SURFACE STRAIN COMPONENTS (PARALLEL* PERPENDICULAR* Z OR HOOP) ELASTIC SURFACE STRESS COMPONENTS (PARALLEL* PERPENDICULAR* Z OR HOOP} SURFACE STRESS INTENSITY, SU^f XCZ VON MISE5 EQUIVALENT STRESS LINE X-L SURFACE X-L STRESS CONDITIONS (PRINTED ONLY IF x£YSUS(2) = 2) -tSAHE AS LINE I-J.ASQVE 3UT APPLIED TO FACE X-D LINES 3 ANO 4 NON-LINEAR SOLUTION (PRINTED ONLY IF X13 IS GREATER THAN ZERO ON CARD CI) £?SL 4 4F10.7 ELASTIC STRAIN COMPONENTS CX,Y,XY,Z) EPPL - 4 4F10.7 PLASTIC STRAIN COMPONENTS (X,Y,XY,Z) LINE 3 NON-LINEAR SOLUTION (CONTINUED) eporig 4 4f10.7 shift of origin of stress-strain curve due 70 Previous loao cycles spgen 1 f10.7 equivalent strain PC5G£N 1 F10«A EFFECTIVE P0ISS0NS RA7I0 SIGE 1 F10.2 EQUIVALENT STRESS NOTE I - STRESSES AND STRAINS ARE PRINTED AFTER THE PLASTICITY CORRECTIONS. NOTE 2 - FOR AXlSYNMETRIC SOLUTIONS, THE X,Y,XY» AND Z STRESS ANO STRAIN OUTPUTS CORRESPOND TO THE RAOIAL, AXIAL, IN-PLANE SHEAR * AND HOOP STRESSES ANO STRAINS, RESPECTIVELY. T STRAIN 1 3 F3.0 3F10.7 STRESS 3 3F3.0 2 2F9.0 35 TABLE 5.13 INTERFACE ELEMENT - TJQ DIMENSIONAL SUBROUTINE NAME NO. OF NOOSS PZri ELEMENT CEGREE3 0?" rS£S30H PER NOQE REQUIRED REAL CONSTANTS TEMPERATURES P PES SUP £3 MATERIAL PROPERTY EQUATIONS MATRICES CALCULATED PLASTICITY FCRCFS SAVED ON TAPE KEYSU8<1> <EYSti8<2) STIF12 2 2 I.J UX»U7 TH£TA*STIFFNESS* INTERFERENCE* START. A NEGATIVE INTERFERENCE ASSUMES AN INITIALLY OPEN GAP IT START = 0.0 OR 5LANX, PREVIOUS CONDITION CF SAP DETERMINED FROM INTERFERENCE IF START = 1.0* GAP PREVIOUSLY CLOS ANO NOT SLIDING IF START = 2.0. GAP PREVIOUSLY CLOS AND SLIDING RIGHT IF START => -2.0 » GAP PREVIOUSLY CLOSED ANO SLIDING LEFT IF START = 3.0» GAP PREVIOUSLY OPEN T(I) ,T(J) HU SUBROUTINE DATE STIFFNESS NO (NON-LINEAR ELEMENT) 2 NORMAL FORCE(FN)» TANGENTIAL FORCECF - NO STIFFNE35 ASSOCIATED WITH SEPARATED INTERFACE 1 - STIFFNESS»I.0E-<5 ASSOCIATED WITH NORMAL STIFFNESS FOR SEPARATED INTER FA.CZS AND WITH TANGENTIAL STIFFNESS FOR SLIDING INTERFACES - CONVERGENCE 3ASED ON UNCHANGING ElEME> STATUS 1 - CONVERGENCE BASED ON CHANGING ELEMENT STATUS WITHIN A 5 PERCENT TOLERANCE C HU 2 - CONVERGENCE 3ASED ON CHANGING ELEMENT STATUS WITHIN A 10 PERCENT TOLERANCE MU <*/0W72 86 TASLE 5.14 INTERFACE. ELEMENT - TWO DIMENSIONAL . ELEMENT PRINTOUT EXPLANATIONS EXPLANATION ELEMENT NUH3E5? NOOES I ANO J GAP SIZE* SLIDING DISTANCE NORMAL FORCE TANGENTIAL FORCE ELEMENT STATUS 1 - GAP CLOSED, NO SLIDING 2 - SLIDING CONTACT (NOOE J MOVING TO RIGHT Or NOOE I) -2 - SLIDING CONTACT (NCOS J MOVING TO LEFT OF NOOE I) 3 - GAP OPEN OLD 1 12 KlyPE VALUE" OF THE PREVIOUS ITERATION NUH8ER OF LA3FL csnsta.s iTS FORMAT EL EM 1 15 NQOE5 2 2IS US£?,USLIDE 2 2F9.S FN 1 G13.5 FS 1 G13.5 KTYPE 1 12 87 z I -^— Y MOTE - Surface stressas ara available on faces -2 and 4. (Surface coordinate system shewn) Figure 5.1. Three -Dimensional Isoparametric Solid Element Z M Figure 5.2. Three-Dimensional Isoparametric Solid Element Output 88 Figure 5.3. Three-Dimensional Interface Element. > I F n Slope = k/10 6 if KEYSX3B(1)=1 . ■ A* ( u n)j-< u n)l + ' GAP /i "IN Slope=k/lO or* KEYSUB(l)=l T ±5% tolerance if KEYSUB(2)=1 >• (usJj-^sJj - USLIDE ^I F «i for F < n Figure 5.4. Three-Dimensional Interface Element Output 89 (or Axial ) Q - Convection Face Numbers Heat flow out of the element is positive (or Radial) Figure 5.5. Isoparametric Quadrilateral Temperature Element 90 (or Axial ) ->— X (or Radial) Figure 5.6. Two-Dimensional Conducting Ear Element 91 ( or Axial £\ - Face Numbers Surface Stresses are available on Face 1 and Face 3. X (or Radial) Figure 5. 7 . Two -Dimensional Isoparametric Element (or Axial) t*— X (or Radial) Figure 5.3. Two-Dimensional Isoparametric Element Output 92 Y ar Axial) I INTERFERENCE CONDITIONS I I *■ 8 determines element orientation I * T(I) Nodes may be coincident (or Radial) ■£ 1 5 »' S<° +-= •-— o -*}s>oh- RIGHT SLIDE (KTYPE OR START = +2) Figure 5.9. Two-Dimensional Interface Element SLOPE = k/10 6 IF KEYSUB(1)=1 c*,j.-<«v,) x -j Fl SLOPE = k/10 IF KEYSUBI iYSUB(l)=l 2 Cu,l -Cu,) x - usuioe - M\F^ ( For F« < O Figure 5.10. Two -Dimensional Interface Element Output 93 CHAPTER 6 CONCLUSION The manual for ANSYS for analysts of anchored pavements has been prepared to provide the user a ready reference for analyzing the re- sponse of anchored pavement system subjected to vehicle static loads, moisture variation, and temperature variations. The manual is prepared so that it can be used with a minimum num- ber of references. For preprocessing, Chapter 3 provides the details of a program developed at I IT called FEMESH. The User's Guide for ANSYS has its own preprocessing subroutines, however, the FEMESH is more efficient for preprocessing the anchored pavement system. If any postprocessing Cpost-plotting) is desired, the User's Guide for ANSYS should be consulted. In the particular analysis performed, postpro- cessing was not utilized as plotting was done by hand. The computer program provides the numerical values of stresses, strains, deflections in all elements of various materials. There is no practical limit of restriction of material numbers, that is the program can be used with different materials in any direction. For heat transfer, the program provides the distribution of temperature versus time at any point. ANSYS in general has the capability of obtaining response of the pavement system under transient dynamic loads, however, this has not been incorporated in this manual. The most noteworthy point for the ANSYS program is the wave front solution and certain limitations caused by the said solution. The ordering of nodes therefore must be done to minimize the size of wave front as has been explained in detail in Chapter 4. The program has been found versatile and capable of solving complex geometrical struc- tures resting on complex geologically earth mass. 94 REFERENCES 1. Bathe, K.J. and Wilson, E. L. , "Numerical Methods in Finite Element- Analysis," Prentice-Hall, Inc., (New Jersey, 1976. 2. Cook, R. 0., "Concepts and Applications of Finite Element Analysis," John Wiley and Sons, New York, 1974. 3. Desai, C. S. and Abel , J. F, , "Introduction to the Finite Element Method," Von Nostrand Company, New York, 1972. 4. DeSalvo, G. J., "ANSYS Verification Manual," Swanson Systems Inc., 1976. 5. DeSalvo, G. J. and Kohnke, P. C. , "ANSYS Introductory Manual," Swanson Analysis Systems Inc., 1975. 6. DeSalvo, G. J. and Swanson, J. A., "ANSYS Examples Manual," Swanson Analysis Systems Inc., 1972. 7. DeSalvo, G. J. and Swanson, J. A., "ANSYS User's Manual CRevision 2)," Swanson Analysis Systems Inc., 1975. 8. DeSalvo, G. J. and Swanson, J. A., "ANSYS User's Manual CRevision 3)," Swanson Analysis Systems Inc., 1978. 9. FORTRAN Extended Reference Manual, Publication Mo. 60497800, Control Data Corporation. 10. Guyan, R. J., "Reduction of Stiffness and Mass Matrices," AIAA Journal , Vol. 3, No. 2, Feb. 1965. 11. INTERCOM Reference Manual, Publication No. 60494600, Control Data Corporation. 12. Irons, B. M. , "A Frontal Solution Program for Finite Element Analysis," International Journal for Numerical Methods in Engineering , Vol. 2, No. 1, Tan., p.p. 5-23, (Discussion May , 1970, p. 149), 1970. 13. Jones Jr., R. F. and Costello, M. G. , "A Solution Procedure for Nonlinear Structural Problems," . Numerical Solution of Nonlinear Structural Problems , ASME, pp. 157-169, 1973. 14. Kohnke, P. C. , "ANSYS Theoretical Manual," Swanson Analysis. Systems Inc. , 1977. 15. Kohnke, P. C. and Swanson, J. A., "Thermo-Electric Finite Elements," International Conference on Numerical Methods in Electrical and Magnetic Field Problems, Santa Margherita Ligure, Italy, June 1-4, 1976. 95 16. Lekhnitskii, S. G. , "Theory of Elasticity of an Anisotropic Elastic Body," Hoi den-Day, San Francisco, 1963. 17. Loader Reference Manual, Publication No. 60429800, Control Data. Corporation. 18. Melosh, R. J. and Bamford, R„ M. , ''Efficient Solution of Load-Deflection Equations," Journal of the Structural Division , ASCE, Vol. 95, No. ST4, Proc. Paper 6510, pp. 661-676, CDiscussions, Dec. 1976, Jan., Feb., May 1970, Closure Fed. 1971), April 1969. 19. NOS/BE Reference Manual, Publication No. 60493800, Control Data Corporation. 20. NOS/BE Users Guide, Publication No. 60494000, Control Data Corporation. 21. Przemieniecki , J. S., "Theory of Matrix Structural Analysis," McGraw-Hill, 1968. 22. Ralston, A. and Wilf, H. S., "Mathematical Methods for Digital Computers," John Wiley & Sons Inc., New York, 1962. 23. UPDATE Reference Manual, Publication No. 60449900, Control Data Corporation. 24. Wilson, E. L. , Taylor, R. L. , Doherty, W. P., and Ghaboussi, J., "Incompatible Displacement Models," Numerical and Computer Methods in Structural Mechanics , Edited by S. J. Fenves, et al . , Academic Press Inc., New York and London, pp. 43-57, 1973. 25. Zienkiewicz, 0. C. , "The Finite Element Method in Engineering Science," McGraw-Hill Company, London, 1971. 96 APPENDIX A NOTATION The notation defined below is used throughout the appendices B and C. General Tzrzi Meaning [3] Strain-displacement matrix [C],[CJ Damping matrix, thermal damping matrix [D] Stress-strain matrix E Young's modulus {F} Force vector [K],[K] Stiffness matrix, conductivity matrix [H] Mass matrix {Q} Heat flow vector {T> Temperature vector [T R ] Local to global conversion matrix u,v,w,{u} Displacement, displacement vector dtl Virtual internal work 6V Virtual external work x,y,z Element coordinates X,Y,Z Nodal coordinates (usually global cartesian) a Coefficient of thermal expansion z Strain v Poisson's ratio c Stress 97 Superscripts and Subscripts on [ML ("CL'TO, (u>, {T}, and/or (F) No subscript implies the total matrix in final form, ready for solu- ti on . a nodal effects caused by an acceleration field c convection surface cr creep e based on element in nodal coordinates g internal heat generation l based on element in element coordinates Id large displacement m master n nodal effects caused by externally applied loads pi plasticity pr pressure s slave sw swelling t thermal — (bar over term) heat transfer matrices (flex over term) reduced matrices and vectors (dot over term) time derivative 98 APPENDIX 3 ANALYSIS PROCEDURES This section of the manual is designed to give users an understanding of the theoretical basis of each analysis type. The derivation of the individual element matrices and vectors is discussed in Appendix C. In the matrix displacement method of analysis based upon finite element idealization, the structure being analyzed must be approximated as an assembly of discrete structural elements connected at a finite number of points (called nodal points). If the force-displacement relationship for each of these dis- crete structural elements is known (the element "stiffness matrix") then the force-displacement relationship for the entire structure can be assembled using standard matrix methods. Figure Bl gives a summary of the ANSYS analysis procedures available and may be used as a guide in selecting which type to use. Each of the analysis procedures is described in the following sections. STATIC ANALYSIS The overall equilibrium equations for static analysis' are: [K]{u> = {F} (B.l)' N where: [K] - total stiffness matrix - Z [K ] m=l e {u} = nodal displacement vector N - number of elements C'O = element stiffness matrix (may include the element stress stiffness matrix^ 99 f start) TRANSIEHT AND STEADY STATE THERMAL ANALYSIS SUCKLING ANALYSIS (:<a,n-t) I NON-LINEAR TRANSIENT DYNAMIC ANALYSIS C<AN»<M REDUCED LINEAR DYNAMIC TRANSIENT ANALYSIS (JCAN-S) HARMONIC RESPONSE IS (XAN-3) ^-ANALYSIS REDUCED HARMONIC RESPONSE ANALYSIS ( KAN-6 ) MODE FREQUENCY - ANALYSIS (JCAN-2) <AN is tha '<ay input on tha CI card to select the analysis type Quasi -Linear - the only non-linearities peraittad ara caps. Figure Bl. Summary of ANSYS Analysis Types 100 {F}, the total force vector, is defined by: •{F} = {F n } + (F a ) + Z ({F*}-+ (Ff > + {F? 1 } + {Ff } + (Ff } + {Fl d » (3.2; e a where: {F } = applied nodal load vector {F } = [M]{A } = acceleration load vector N [M] s total mass matrix 2 [M ] m=l a [M ] - element mass matrix {A } = nodal acceleration vector (FT = element thermal load vector e {F^ } = element pressure load vector CF? } = element plastic strain load vector e {F } - element creep strain load vector {F } = element swelling strain load vector e {F } = element large displacement load vector The same definitions used here apply to all other analysis procedures except heat transfer analysis. If sufficient boundary conditions are specified on {u} to guarantee 2 unique solution, equation 3.1 can be solved to obtain the nodal point dis- placements at each node in the structure. The simultaneous equations with all degrees of freedom (including those with specified displacements) are given in equation 3.3. 101 :< K r <r T K rr / > r \ F. V (B.3) L J The subscript r is associated with the reaction forces. Mote that {u } H is known, but not necessarily equal to {0}. The top half of equation 3.3 inay be solved Tor' luj-r {u} .= -[;<]- '[^{u^ + [K]"'{F} The reaction forces {F } may then be computed from the bottom half of equation 3'. 3 ; (F r > » c^fcu} + [;< rr ]{u r > (B.5) These reaction forces should always be in equilibrium with the applied loads. The following circumstances could cause a disequilibrium, usually a moment disequilibrium: 1. The presence of stress stiffening Mote that moment equilibrium is not preserved/ •"Hits may. be accounted for as as implicit updating of the coordinates. 2. Tne presence of four-noded shell elements where the four nodes do not lie in a flat plane. 3. The presence of nodal coupling or constraint equations. The user can write any form of relationship between the displacements, and these may induce fictitious forces or moments. Thus, the reaction force printout has been used to detect input errors. 102 1.3 HEAT TRANSFER ANALYSIS (KAN=-1) Steady stats and transient heat transfer problems may be solved by finite element techniques analogous to those used for structural analysis. A. Steady State The basic thermal equilibrium equation is: ro<T}.--tQ) (B.6) where: [K] ■ thermal conductivity matrix -CQ} = heat flow vector {T} - vector of the nodal point temperatures This equation is identical in form to equation B.l for static analysis. If the material properties and film coefficients are not temp- erature dependent, equation B.6 can be solved directly with one iteration. If the material properties (or film coefficients) are temper- ature dependent, they are evaluated at the temperature of the previous iteration. The procedure used is shewn in Figure B2. An optional convergence criterion is available with steady- state analysis. All nodes are monitored for the largest change in temp- erature. If this largest change is less than the criterion,, then the solution is said to be converged. This criterion is input on the MD card (TCV) and defaults to 1.0 degree. 103 (Stjrt) Set all temperatures equal t0 T UNIF (l ' nput quantity) Evaluate [1] p- 4 i Solve for {7} Figure B2. Flow chart for Steady State Heat Transfer Analysis with Temperature Dependent Material Properties. B. Transient The basic thermal diffusion equation is: [C]{T } + [K]{T} = {Q} where [C] is the specific heat matrix. (B.7) 104 The form of this equation is .identical to the non-linear dynamic transient equation (KAN-4) except that the mass term is not present. For temperature dependent material properties (or film coefficients), the eval- uation of the properties is made at a temperature extrapolated from the previously calculated temperatures. The time-integration schemes are also the same as that of the non- linear transient dynamic analysis type (KAN=4) except that the options offered are one order lower, i.e., linear (KAY(2)=2) and quadratic (KAY(2)=0 or 1, the recommended usage). The linear (first order) equation is: (^-[C] +'TO){T t > = {Q(t)> + CC]{T t-1 ) ^- (B.3) The quadratic (second order) equation is: ( 2At n + At, t -St^^Cc] + raja t > = (Q(t) ) + where: t Q ■ present time t, = previous time t~ = time at second previous time At, - V fc 2 T, ■ temperature at this time step (to be calculated) T. , = temperature at previous time step (known) T t 7 - temperature at second-previous time step (known) 105 The starting procedure of the transient thermal analysis is as follows: If the first load step is run at time = 0. (TTME=0. on L card), a steady-state analysis is performed at that time. Alternatively, if the first load step is run at time > 0. (TIME > 0. on L card), all temperatures at time = 0- are set equal to TUNIF. The temperatures at time = £, (t. means the solution at time i) are determined by the user selected time interpret- ation procedure- (linear or quadratic, depending on the value of KAY(2J). If the quadratic integration is used, it is started by setting all temperatures at a previous time point (t ,) to those values at time = 0. It is not recommended that the time step size between adjacent d 2 J iterations be changed by more than a factor of ten, unless — j is very • d-T smal 1 . An option is available to increase the time step size automatically if the rate of change of temperature at all nodes is less than an input criterion. This optimization criterion is input on the MD card as TOY, which defaults to 5.0 degrees. Using the default value, this criterion may be expressed as: max d*T ,.2 d-r < 5, (3.10) Because a history has to be developed, the time step size may be increased only after the second iteration. 106 APPENDIX C ELEMENT LIBRARY Each element In the ANSYS program is discussed in this section. The assumptions required to generate the element matrices and load vector are given,, including the assumed shape functions. Certain aspects are also dis- cussed' in the chapters on the nonlinear capabilities of ANSYS. Elements with nonlinear material properties (plasticity, creep, and/or swelling) have appro- priate quantities saved at the integration points, except as noted. In broad terms, all stress and thermal elements have their appro- priate matrices and vectors derived using the procedures in the following two sections entitled: Virtual Work Derivation for Stress Analysis Elements. Virtual Work Derivation for Thermal Analysis Elements. These derivations assume the use of an isoparametric element* as that element family is one of the simplest. On the other hand, a complete virtual work derivation is also given with elements STIF46, STIF53, and STIF61 , which are not isoparametric elements. Virtual Work Derivation for Stress Analysis Elements . The principle of virtual work says that a virtual (very small) change of the internal strain energy must be offset by an identical change in external work due to the applied loads, or: 6\J = 5 V (C.l) where: $ u = virtual strain energy (internal work) 5 V ■ virtual (external) work 107 "he virtual strain energy is {o-} 1 {a} d(vol) vol (C.2) where: {s } = strain vector {a} - stress vector vol = volume of element The stress is related to the strains by: M = [D](u> - { £th }) (C.3) where: [D] = material property (constitutive) matrix te+u} ~ thermal strain vector Equation C,3 ' may also be written as (s}= a th ) + [orV) (C.4) For the case of three-dimensional solid elements, equation- (2.0.4) may be exoanded to: r ~\ r ^ £ x V T £ y a AT y S z V _ J a AT Y xy r ~ ] y xy V At V. -/ ^ J y + E -? r xy xz \- - f^- E y E z _^x ™ i Q E y u z ; xy 1 ~— G yz Q 1 xz < V (C5) xy 'yz T xz 108 /■/here AT - the difference at the point in question between its own temperature and the reference (strain free) temperature (TREF). The [D] matrix is presumed to be symmetric, so that: J£X s _X£ E x E y (C.fi) ZX _ XZ (C7) (C.3) Thus, in terms of ANSYS input variables: [D] -1 1 EX NUXY EY NUXZ EZ NUXY EY 1 EY NUYZ EZ NUXZ EZ NUYZ EZ 1 EZ 1 GXY 1 GYZ 1 GXZ (C.9) and: {£ th> = < 'alpxutP ALPY(aT) ALPZ(aT) > (CIO) 109 If GXY, GYZ, and GXZ are not input, they are computed as rvv - ^X EY (r in Ga/ " £X + £Y + 2 NUXY EX l j G7Z S £Y + £Z + 2 NUYZ £Y (C ' 12) GXZ S cv , C->" ■ % UIIV-7 -V ( C . I 3 , EX + t£ + 2 NUXZ cX A further comment on the [D] matrix: It must be positive definite. This condition is always met if the material is isotropic or NUXY, NUYZ, and NUXZ are all zero. But, for example, if EY is less than c-r equal to 2 EX (NUXY) , the material is not positive definite. {e- ) may also be considered to include plastic, creep, and swelling effects, where applicable. Equations C.2 and C.3 are combined to give: <5U = J ({6£} T [0]{£> - {o£} T [D]{ £th » d(vol) (C14) -'vol The strains may be related to the nodal displacements by: U> - CB]{u} (C.15 where: [B] - strain-displacement matrix {u} - nodal displacements Combining C.15 with C. 1 4 ., and noting that {u} does not vary over the volume: <5U =-(u} T [3] T [0][3j{u} d(vol) vol - (u} T f [3] T [0]U th } d(vol) (C.16) vol 110 Next, the virtual work will be considered. The inertia! effects will be studied first: «V-I {Sw^UfVvoI)} d(vol) (C.T7) J vol where: {w} « vector of displacements of a general point {r } ■ acceleration (D'Alembert) force vector According to Newton's second law. 7or = PiT {W} . «-T8> where: p - density t ■ time The point-wise displacements are related to the nodal displace- ments by: w - [A] u (C.19) where [A] - matrix of shape functions. Combining equations C.18 and*CiT9": 5V = {5u} T p I [A] T [A] d(vol) Wu} (C20) -/vol 3t The pressure force vector formulation starts with: 5V = I {5w} T {p} d(area) (C.21) -' area where {p} - the applied pressure vector (normally contains only one non-zero component). Ill Combining equations 5V = {6u> T f [A] T { P } d(area) (C.22) area Finally, equations combined to give: {5 a} 7 [3] T [D][3]{u> d(vol) Jvol - (3u} T [3] T [0]{s: th } d(vol) ^YOl - {ou} T p [A] T [A] d(vol) |r {u} + {<5u 7 }p J [A] 7 d(area) (C.23) -* area Noting that the {00} is common in all of the above terms, and that its terms are independent of each other, it may be cancelled out. Thus, equation C.23 reduces' to":""' DC e ]{u} - {F^} = [M e ]{u> + {?l r } (C.24) where: [K ] = I [B] [D][B] d(vol) = element stiffness matrix e Jvol ir } * I [3] [0]{£^u> d(vol) = element thermal load vector e J vol * [M«] = p I [A] [A] d(vol) = element (consistent) mass matrix ' e J vol . .2 {u} =fr-{u}= acceleration vector (such as gravity effects) a U ny I T {F* } - [A] {p> d(area) = element pressure vector J area 112 Those elements which use a lumped sum mass matrix rather than a consistent mass matrix are noted with the individual element description. The element stresses are computed by combining equations C.3 and c.15 to jet: M - CD]([B]{u} - { £th » (C.25) Mote that [S] is the strain-displacement matrix that must be specialized for each stress calculation point (centroid, integration point, node point, etc,} Virtual Work. Derivation for Thermal Analysis Elements As before, the basic expression of virtual work is: SU = sV where: 511 = virtual internal work 5V s virtual external work In thermal terms, the virtual work within one element is: <5U (C.26) - I (5S> T -'vol {Q v > d(vol) (C.27) where: C 3T(x,y,z) ax (S>< J 3T(x,y, 2 ) 3T(XvY,z) > - vector of temperature v 3Z IP s x WJ=< > = vector of heat flows v. Q «J 113 7(x,y,z) = temperature at point x,y r z Q = heat flew in the x-di recti en per unit area Q- = heat flew in the y-di recti on per unit area Q_ = heat flew in the z-di recti an per unit area The heat flows are related to the temperature gradients by: wnere: <Q.,i ■ [0]{S} [D] - KYY , KZZ (C.2S-) The temperature distribution within an element is based on the assumed temperature shapes: T(x,y,z) = (M}'{T } (C.29, where: {N} = vector of shape functions {!'} = nodal temperature vector e Then, {S} is related to {7 } using the definition of {S> and equation C.29 to give: {S} = [3]{T e > (c.3a) wh ere [B] = {— } T l 3y ' T T { iN } l 3X ; Combim'na ecuations ■ C.27, C.28, and C20 and realizing that 114 the nodal temperature vector does not change over the volume of the element, ? r [b] t i Jvol «U s {ST.}' [B]'CD][B] d(vol) {T } (C.31) e Jvol e Next, consider the virtual internal work associated with con- vection surfaces: ..] 5AT Q d(area) (C.32) area where n = :i the direction normal to the surface. AT is defined by: AT = T(x,y,z)| - T B (C.33) where: T(x,y,z)| - the temperature function evaluated at the s convection surface T„ s temperature of the coolant (bulk temperature) Note that T„ is a constant so that SAT -«T(x,y,z)| (C.34) s The heat flow over the unit area is defined by: Q n = h f AT (C35) where h f = film, coefficient for heac. transfer of the surface. Combining equations C.29, C.32, C.33, C.34, and c.35, and noting that {T g } does not vary over the surfaced arid that Tg and h f are. assumed not to: 115 oU*{oT e } T h f 1 {N| } T d(arga)-{T e > area s -C5T e > T h f T 5 f {N| > d(area) (c.36) -/ area where {N| } are the shape functions evaluated at the convection surface, s The internal heat generation rate effect is included by con- sider? na: 5V -- J oT(x,y,z) q d(vol) (C.37) where "of = the heat generation rate per unit volume. Combining equations C.29 and C.37 and real vz4"ng- that the nodal temperatures vector (T } does not change over the volume of the element, and assuming that of does not chance over the volume of the element, 5U={dT 8 > T q j {N} d(vol) (C.38) J vol The virtual internal work associated with a change of stored energy is: 5U = I 5T(x,y,2)y d(vol) (C.39) -'vol 3 T f x v 7 ) where: y = pC — ' lV~ ! -• total heat change per unit volume per P 3 C unit 'time p = density C = specific heat t = time 116 Combining equations C.29 and C.39 and noting that {T } does not vary over the element, and assuming that p and C do not vary over the P element, oU = (6T e } T pC p J vol oU = (6T e } T pC p J (N}{N} T d(vol) {t a } (C.40) where { y = ^ ty The effect of the nodal heat flows may be considered by, 5V » (oT e } T {Q e ) (C.41) where {Q } is the nodal heat flow vector. Combining equations C.26, C.31, C.36, C.38, C.40, and C.41, and noting that since {<5T } is an arbitrary set of virtual temperature changes which may be cancelled out, [K a ] + [K^] (y + [Cj{y = {Q^} + {Qp + {Q e } (C.42) where: [K fi ] = J [B] T [D][B] d(vol) 70 = total element conduc- [K?] = h f f (NL HNL } T d(area) tivity matrix e T y area [C ] ■ PC J {N}{N} T d(vol) = specific heat (thermal e " vol damping) matrix {Q e } = h f T BjT {N I S } d ( area ) area = total element heat rn q, ••• r ,.,, ,/ ,x flow vector CQ«} = q / {N} d(vol) e Aol This is the final temperature heat flow equilibrium equation. The above definitions are used to develop the element matrices and vectors 117 ■ STIF12 - TWO-DIMENSIONAL INTERFACE ELEMENT The displacement functions for the interface element can be sep- arated into the normal and tangential directions because they are basically independent. Tn the normal direction, when the normal force (F ) is negative, the interface remains in contact and responds as a linear spring. As the normal force becomes positive, contact is broken and no force is trans- mitted; unless KEYSUB(1)=1 , in which case asmall force is supplied to prevent a portion of the structure from being isolated. In the tangential direction, for F < arid the absolute value of the tangential force (F ) less than or equal to (p|F |), the interface does not slide and responds as a linear spring in the tangential direction. However, for F„ < and F > u|F I , sliding occurs. Note that F„ is a n s ' n 1 s variable and if contact is broken, the tangential function degenerates to a zero slope straight line through the origin Cor of slope K/10 , if KEYSUBO)=l) indicating that no Cor little) tangential force is required to produce sliding. These may be related to each other by y|F | * K(u - u - u , . . A where u .. . is the distance of sliding. Figure s, s, slide) slide C2 shows ■" the; force-deflection relationships for this element. Figure CI . 118 SLOPE-* K/10° If KEYSUB(l) = 1 j) L («„} - («„) - 4 :» ulF. SLOPE =■ K/10 If KEYSU3(1) = 1. 1 (O - (u ) s J s I -U r For F < and for n initial loading Figure C2. STIF12 Force-Oeflection Relations STTFI2 may have one of three conditions: in contact and not sliding, in contact and sliding, or open. The following matrices are derived with the assumption that 9 (theta) is input as 0.0. 1. In contact and not sliding - The resulting equilibrium equation is: L K -K K -K K -K stiffness matrix -K K U s,I 'n.I r sl nl r *\ " Ku o -KA <i r a -s f + i r (c ' 43) n 's,J ^ n,Jj sJ n nJ Ku. KA Displace- Applied Element Load ment Nodal Vector Vector Force Vector 119 where K = A = F = n input stiffness interference normal force across gap distance that nodes I and J have slid with respect to each other 2» In contact and sliding - In this case, the element equilib- rium equation is: K -K -K K Stiffness Matrix r, < 's,I l n,I 's,J si >=< vVi nl sJ uF. F n I. nJ -KA -pF r KA Displace- Applied Element ment Vector Modal Load Vector Force Vector where y = coefficient of friction. (C.44) 3. Open - When there is no contact between nodes I and J, the stiffness matrix and load vector are null matrices. The stress pass of STIF12 always uses the latest possible informa- tion concerning gap status. Therefore, for non-cnnverged iterations, it may not agree with the reaction forces which are based on the previously calculated stiffness matrix and load vector. 120 STTF32 - 2-0 CONDUCTING 3AR ELEMENT The temperature function is a linaar polynomial of the form: T(x) = C 1 + C 2 ; (C.45) wn ere the element x-axis extends along the element axis STTF42 - 2-0 ISOPARAMETRIC SOLID ELEMENT The 'displacement shape functions are repeated here for convenience, A local: coordtnats-s&sSem fs developed as shown -in Figure C3: Y.v (-1,1) (1,1) (-1,-1) (1,-D X,u Figure C3. Local Coordinate System 121 It is seen that s and t vary between -1 . and +T. The basic, isoparametric shapes yield the following set of shape functions: U b (s,t)- = 1(1 - S)(l - tJUj + ^{1 + S)(l - t)Uj + \0 + s)0 + t)u ;< + Itf - s}(l + t)u L (C.46) v b (s,t) = 1{1 - s)(l - t)Vj + 1(1 + S)(l - t)Vj . 1 1/, ^■0 + s)(i + t)v ;< -i(i . sjq + t)v L (C.47) Mote that these shapes do not permit the edges to bend. The extra (and optional) shapes are defined as u e (s,t) = (1 - s^Cj + (1 - t 2 )c 2 v e (s,t) = (1 - s 2 )c 3 + (1 - t 2 )c 4 (C.48) (C.49) Their effect may be seen in Figure C4. c, through c, may be referred to as node! ess variables. The total displacements are then: u - u. + u d e v - v b + v e (C.50) (C.51) Without extra shapes With extra shapes fi- gure C4. Effect of Extra Shapes 122 These displacement shapes are used to' generate a 12 by 12 stiffness matrix. This matrix is then condensed to an 3 by 3 matrix, because there are only 3 decrees of freedom to connect to the rest of the structure- The condensation is analogous to that associated with superelement generation. The Toa <j vector "is also generated .with- TZ. terms and. is then: condensed to a. The mass matrix Ts consistent and is' generated as an- 8.. bf.£- A 3 by 3 lattice of integration points is used with the numerical (Gaussian) integra-tion procedure. Note that the extra shapes permit a parabolic deformation along an element edge. Normally this is helpful in modeling a structure, but occasionally it may cause a problem because of the incompatibility at the adjoining edges of two different elements, i.e., a gap opens up or the material "doubles up". The usage of the extra shapes is discussed in greater detail in the User's Manual. The extra shapes are automatically deleted if nodes K and L are the same (i.e. a triangle). This case then gives the same results as a constant strain triangle. The centroidal, integration point, and node point stresses' are com- puted by the procedure described at the beginning of this chapter (£quaticn c. 25 •] Surface stresses may be requested for elastic isotropic materials. Even though the development given below includes some orthotropic effects, it is only valid for a few special cases of orthotropic materials. The surface stresses for plane stress applications, are calculated by: 1. Computing the strain parallel to the fr^e surface: u '- U T - u , I L x \C.zZ) 123 Where: u s displacement parallel to the free surface L = distance between the two surface nodes a * coefficient of thermal expansion (ALPX) AT s difference between average surface temperature and the reference temperature. 2. Setting the stress normal to the surface (a-) to the applied pressure. 3. Setting the stress in the z direction (a-) to 0. 4. Solving for the remaining three quantities of interest (e 2 , £-, a, ) by use of the material property relationships. Specifically: °1 " e l h + v xy °2 (C - 53) 6 3 = " v xy (ff l + ff 2 )/E ; (C.54) e 2>('2- u xy e l )/E a {C - 55) where: E, = (E, + Ej/2. a A j E = Young's modulus in the* x-di recti on (EX) E = Young's modulus in the y-direction (EY) v - Poisson's ratio (NUXY) *y For the axi symmetric option, steps 1 and 2 above are the same. Continuing, 3. Computing the hoop strain (£3): T T T U T + U J % 124 where: u, = radial displacement of node I u, = radial displacement of node J u g - radial displacement of the midpoint of side I- J due to the applicable extra shape function R s radius of the midpoint of side I- J a^ s coefficient of thermal expansion in hoop direction (ALPZl 4. Solving for the remaining three quantities of interest (e^* a i » a-) by use of the material property relationships. Specifically, a - £ 3 E z+ ( V+"xz v xy )q 2 + £ fxz E a (C.57) 3 1 '* E. -it a, s £, E. + a„v + a-,v -f— (C.58) « =!i- v !l- v !i (C.59) e 2 E a u xyE a VE 2 where: E s input quantity (E2) v ■ input quantity (NUX2) v = input quantity (NUYZ) Plane strain analysis is the .same as axisymmetric analysis,, except that step 3 is modified so that simply, e 3 = -a AT (C.60) 125 STIF45 - 3-0 ISOPARAMETRIC SOLID ELEMENT The element formulation includes incompatible displacement modes. A complete description of this technique is the three-dimen- sional extension of STIF42. Either a 3x3x3 or a 2x2x2 lattice of integration points is available for use with the numerical (Gaussian) integration procedure. For nonlinear material properties (plasticity, creep, or swelling), a 2x2x2 lattice is automatically used. The principal stresses are calculated from the cubic equation: x xy T xy a y ' a 'xz yz T xz T yz a 2 ~ a = (C.61) The three computed values of a are the three principal stresses 126 STIF52 - 3-0 INTERFACE ELEMENT The Toad-deflection relationships for the interface element can be separated into the normal and tangential directions since they are basically independent. In the normal (element x) direction, when the normal force (F ) is negative, th& interface remains in contact and responds as a linear spring. As the normal force becomes positive, contact is broken and no force is trans- mitted (unless- KEYSU3(1 )=1 > then a small force is supplied to prevent a portion of the structure from being isolated). In the -tangential directions, for F < and the absolute value of n the .tangential force (F ) less than or equal to (y|F |), the interface does not slide and responds as a linear spring in the tangential direction. How- ever, for F < and F > ^ilF I, sliding occurs. Mote that F is a variable n s ' n ' n and if contact is broken, the tangential function degenerates to a zero slope straight line through the origin (or of slope k/10 , if KEYSUB(1 )=1 ) indi- cating that no (or little) tangential force is required to produce sliding. Figure CS shows' the* force- deflection functions" for this element- F nA Sloce=k/10° if KEYSUBOH (u n )j-(u n ) I+ GAP F s* y|F ! -- Slope=k/10 Q (if :<EYSUB(1) = 1 ±5% tolerance if KEYSU3(2)=1 < u s>j-< u s>i --u F. for F < n .5''' Fiaure Co. Force-Defl ection Rel ationships 127 STIF55 - 2-0 ISOPARAMETRIC HEAT CONDUCTING SOLID ELEGIT The temperature functions used in STTF53 are a scalar form of those developed for displacements in STIF42. First, an element coordinate system is developed as shown in Figure Co. Y i (-1,1) (1,1) .(1,-D (-1,-1) Figure C6~. Element Coordinate System It is seen' that s and t vary between -1. and +1. The basic isoparametric shapes yield the following set of temperature functions: T. Q (s,t) = l/4(l-s)(l-t)T r + l/4(l+s)(l-t)Tj + l/4(l+s)0+t)T K + l/4(l-s)(Ut)T L The extra (and optional) shapes are defined as: T e (s,t) = (l-s 2 ) Cl + (l-t 2 )c 2 (C.52) (C.63) 128 C-, through c- may be r*farr*d to as nodal ass variables. The total temperatures are then: T = T. + T ( c - 64 i d e These displacement shapes are used to generate a 5 by -5 stiffness matrix. A 3 by 3 lattice of integration points is used with the numerical (Gaussian) integration procedure. This matrix is then condensed down to a 4 by 4 matrix, because there are only four nodes to connect to the r^st of the structure. The condensation is analogous to that associated with superelement generation equation,' The load vector -is generated also with six terms and is then condensed down to four. The damping ( specif icfheat) matrix -is consistent and is also reduced down from a 6 by.-.-&.ta.aw4-by 4. 129 APPENDIX D COMPUTER DEFINITIONS AND COMMUNICATION LINKS DEFINITIONS (UNIVAC 1100 COMPUTER) The hardware organization of the 1110 (1100/40) and 1100/80 Systems differ from that of the 1106, 1108, 1100/10, and 1100/20 Systems. In some instances, different terms have been adopted for functionally similar components. In such cases, to avoid confusion and improve readability,, the 1108 term has, as a general rule, been used throughout this document synonymously with the corresponding 1110 term, except where specific comments are made to the contrary. 11 08- type will be used to include the 1106, 1100/10, 1100/20, and 1108. 1110- type will be used to include the 1110 and the 1100/40. The principal corresponding terms are: 1108 CPU ACU Control Introductory Registers (■ Definitions bit Binary digit. value or 1 . the functional CICR) mo 1100/80 CAU(plus IOAU) CPU(plus SPU STU CRS GRS IOU) The fundamental unit of storage having the Bits are grouped in bytes and words to form manipulative units of storage devices. byte A group pf adjacent bits usually operated upon as a unit; can be 6, 9, 12, or 18 bits. buffer On 1100/80 a high speed storage interface (4k to 16k). storage Executive The 1100 Series Executive System. A program that controls or EXEC the execution of other routines. The Executive is the principal interface between the user and the system as a whole. It protects against undesired interaction of users with each other or the operating system. hardware Physical equipment, in the form of mechanical, magnetic, electrical, or electronic devices, as opposed to software. I/O Input/Output. The process of transferring information be- tween the central processor and peripheral, devices. I/O devices include: magnetic tapes, magnetic disks, magnetic drums, CRTs, card readers, printers, and punches. mnemonic Word or term devised so as to aid the human memory. Includes acronyms, such as TTY (telety pewriter) and error mnemonics, such as PWRLOS (powerloss). 130 operating The 1100 Series Operating System. The entire set of system system software available for the 1100 Series which is either a part of or operates under the Executive system. This in- cludes the Executive system proper, compilers, utility programs, subroutine libraries, and so forth. software system user word A set of computer programs including the operating system and user programs, as opposed to hardware. The total 1100 Series hardware/software complex comprising an integrated information processing installation. An individual or organization that consumes services provided by the system. A sequence capable of (a word is Systems). of bits or characters treated as a unit and being stored in a single main storage location represented by 36 bits for the 1100 Series Hardware Definitions ACU applica- tion Availability Control Unit. A device used i n 11 08- type Systems to isolate particular system components for main- tenance or system partitioning. The ACU, in certain operating modes, can initiate autorecovery. The total installation hardware configuration or a subset resulting from partitioning that configuration via hard- ware or software. auxiliary Supplemental storage, as opposed to main storage.' It is storage not directly addressable by CPU(s) and is "accessible only through an 1/0 interface. It includes magnetic tapes, flying- head magnetic drum, FASTRAND drum, disk, or unitized channel storage. break- point CAU central group central site channel A feature whereby the CPU can be stopped or interrupted when a particular main storage address is read, written, or executed as an instruction. Command/Arithmetic Unit. It is the 1110, 1100/40 equivalent of the instruction processing portion of a CPU. A CAU does not contain an input/output section, as does a CPU. There- fore, it must operate in conjunction with an I0AU in order to access peripheral' subsystems. The CPUs, CAUs, IOAUs, IOUs, ACUs, SPUs, STUs, and consoles. The central group, main storage, and attached onsite peripheral equipment in a particular application. A data path for transfer of information between the central group and 1/0 devices. 131 CPU The Central Processor Unit component on 1108 and 1100/80 Systems which executes all control and arithmetic functions. The 1108 System CPU contains an input/output section for access to peripheral devices. CRT Cathode-ray tube display. A television-like device that presents data in visual form. dual Two separate data paths for transfer of information between channel the central group and a subsystem. The sub system control unit must have dual channel capability. IOAU The IOAU controls all transfers of data between the peripheral devices and primary and extended storage. Transfers are initiated by CAU under program control. IOU The IOU controls all transfers of data between the peripheral devices and primary and extended storage. Transfers are initiated by CAU under program control . interface The logical path between two connected nodes. interlock A condition in which a peripheral unit is unable to perform an executable command until the condition is removed by the operator. layered A hardware architecture wherein different parts of main storage storage have different performance characteristics. On the 1110, and 1100/40, this refers to the fact that main storage consists of primary and extended storage. line-id Identification of the communications line -to which one or more remote terminals are attached. Line- id is a unique identifier of one to six alphanumeric characters assigned by the installation. main The general-purpose high speed magnetic core, semiconductor storage or plated wire (1110 only) storage of the system directly addressable by the CPU, CAU, and IOAU/ IOU and serving principally to contain executing programs. mass Auxiliary storage which has random access capability, as storage opposed to magnetic tape, for example. Includes any type of flying-head magnetic drum, FASTRAND drum units, disk, and unitized channel' storage. word-addressable Mass storage which is capable of being mass storage accessed in units of single words in- cluding any flying-head magnetic drum, and unitized channel storage. Word addressable mass storage may be simu- lated on disk. 132 FASTRAND- formatted Mass storage which is accessible in units mass storage of 28 words Cone sector). This may be on actual FASTRAND drum hardware, or may be simulated on other mass storage devices. The term FASTRAND in this manual refers to the format, not the hardware device, unless otherwise stated. This is the most common mass storage format. fixed mass storage Drum, unitized channel storage, FASTRAND drum units, and disk units declared to be fixed during the boot of the system. This storage is considered to be perma- nent (online). MP Multiprocessor. An application having two or more CPUs or CAUs. network All the nodes and interfaces in a system. node A system component. offline A condition in which hardware components are not under direct control of the operating system. online A condition in which hardware components are under direct control of the operating system. P- - Program address register. A CPU control register which register contains the absolute main storage address of the next instruction to be executed. See Appendix A for numeric conversions. peripheral Hardware that is distinct from the CPU, IOAU/IOU and main equipment storage, and which provides the system with increased storage capacity, or with I/O capability. remote Data terminal equipment that is time, space, or electrical! site distant from a central site, and capable of information exchange with the central site via communications lines. site-id Identification of a remote terminal. Site-id is a unique identifier of six alphanumeric characters assigned by the installation to a terminal or group of terminals. SPU System Partitioning Unit. A device used in the 1110 System which permits offline maintenance of units, enables the operator to logically partition the system into two or three independent systems, and can initiate a recovery sequence in the event of failure. STU System Transition Unit. It contains the controls and indicators for partitioning the SPERRY UNIVAC 1100/80 Systems into two independent systems. It also provides an automatic recovery feature and system power control . 133 subsystem One or more peripheral units of the same type, plus a control unit which is connected to an available I/O channel. (.Can be a dual subsystem). symbiont Relatively slow-speed devices, such as card readers, card device "punches, and printers are controlled by symbionts and are used to provide direct input to and output from the system. system The hardward units of a system. They include CPUs, lOUs, conponent CAUs, IOAUs, primary storage, extended storage, control units, and devices and peripheral subsystems. system drjm/ dfsk TTY The mass storage unit to which the Executive is loaded. The system drum/disk is usually unit zero of the specified subsystem. The subsytem of the system drum/disk is specified during system's generation. This specification may be modified by the operator during tape bootstraps. Teletypewriter equipment involving keyboard, printer, and sending and receiving equipment. Used primarily as a demand processing terminal. unitized channel storage Main storage which is treated as and accessed by peripheral I/O hardware. UP Unit processor. An application having a single CPU, or CAU/IOAU. Software Definitions CPU/IOU, backlog The collection of runs which has been entered into the system and are held for facilities availability or unit directed time start. Backlog resides on mass storage. batch A mode in which runs are processed without any basic requi re- process- ment for interactive manual data or controlled input during ing processing. break- The division of symbiont-defined files into parts such that point the output of completed parts may be initiated prior to run completion. This procedure allows more efficient utilization of printers and punches when large symbiont output files are involved. check- Saves the run at a particular point in time for the purpose point of subsequent restart in case of error or interruption. deadline A batch run which is given certain schedule priorities to run attempt run completion by a prescheduled time. 134 demand process- ing file A mode in which run processing is basically dependent on manual interaction (.typically from a remote terminal) "time-sharing". during processing. Commonly known as .An organized collection of data, treated as a unit, and stored in such a manner as to faciliata the retrieval of each individual data item. Files are retained on auxiliary storage devices. catalogued file A file known to and retained by the Executive for a period of time not necessarily related to the life of a particular run, and retrievable by runs other than the run which origi- nally created the file. In some cases, a catalogued file may be accessed simultaneously by two or more runs. A transient file created by, accessible to, and existing within the life of a single run (as opoosed to catalogued file). logical The name associated with a system component. The logical name name is not required to connote the system component with which it is associated. real time A mode of operation in which the system's response to input process- is sufficiently fast to influence the operation being con- ing trolled. In the real time mode the program generally has exclusive use of a CPU/CAU. Generally, real time processing is under the influence of independent inputs from one or more communications devices. The real time mode may be entered from either batch or demand mode. temporary file restart run run- id swapping Resumption of processing a run from a checkpoint rather than from the beginning of the run. A group of tasks prescribed as a unit of work for the system. A @RUN control statement must be the first card or image of a run. A @FIN control statement is the last image. Identifies a run to the Executive. Run- id may consist of one to six alphanumeric characters and is specified on the @RUN control statement. If the specified run duplicates a run- id already in the system, the Executive modifies the newly sub- mitted run- id to make it unique. When the run- id is modified, both the original and the modified run-ids are output to the operator console. The 1100 Series Operating System's method of moving low priority runs from main storage to mass storage in order to provide space to load higher priority runs into main storage for execution. 135 symbiont A complex of Executive routines providing the user interface with symbiont devices. Symbionts buffer the output so that symbiont devices can handle the high speed output which the cemtral processor provides. This allows system processing to proceed at the higher internal and mass storage speeds rather 'than at the relatively slow speed of symbiont devices . TSS Terminal Security System System Definitions bootstrap Act of loading (.booting) the Executive into main storage along with certain other initialization functions which vary depending on the type of bootstrap performed. Boot- strap is used synonymously with boot. initial bootstrap The method wherein the operating sy stem is read from the boot tape and copied onto mass storage devices. At the conclusion of the initialization, the Executive control routines, called the resident Executive, are read into main storage and are given control . recovery bootstrap The method wherein the Executive control routines are read from tape, disk, or drum and copied into main storage. autorecovery A recovery bootstrap of the system taken when a system malfunction or error is detected. The recovery may be system initialed (programmed recovery) or ACuV SPU/STU initiated. Operator intervention is not needed for either type. panic The process of documenting portions of main and mass storage dump for future analysis. Panic dumps are usually initiated by the operator or the Executive following a system error. system The process of tailoring the operating system to the parti - genera- cular hardware configuration and software requirements of a tion site. The end result of a system generation is a tape that contains a copy of the operating system in a form suitable for loading into the computer systam (i.e., a boot tape). zero stop A CPU/CAU stop initiated by the Executive due to either software or hardware detected faults. COMMUNICATION LINKS / The transmission and reception of data to and from a computer require a highly reliable electronic conversion process in most instances In general, data are generated and processed by both terminals and com- puters in coded formats utilizing patterns of binary bits. Transmission 136 of data over communication Tines requires a conversion of data from an electromechanical or magnetic storage format to electrical communication signals . These signals represent tones that are audible only when used to drive a suitable speaker-like or diaphragm device such as a telephone receiver. On receipt, the signals or tones are reconverted to equiva- lent electrical energy to rerecord the data mechanically or magnetically. The devices that perform this conversion process at both the sending and receiving ends of a communication line are known as either modems or Data Sets. (The word "modem" is an acronym for the function "modulate-demodulate." Modulation is the conversion of impulses to tones; demodulation is the reverse) . Data Sets are a specific type of modem installed by Bell System companies. The modem, in effect, is the telephone station through which a terminal talks to the timesharing computer. In most cases, Data Sets include telephone instruments and dials. The actual connection of terminals to modems is accomplished in either of two ways: 1. The terminal can be "hard-wired" to the modem. This indicates that the wiring of the terminal is connected directly into the transmitter/ receiver unit. 2. The modem can incorporate an audio coupler . With this approach, the connection is established between the terminal location and the computer on an ordinary voice- grade dial telephone. The telephone handset is inserted into the audio coupler of the modem, which then generates or reads tones into or from the telephone instrument. The hard-wire installation is more reliable, of higher quality, and of greater permanence. However, this approach requires profes- sional installation, represents a longer-term commitment, and is less flexible. By comparison, audio coupling is more subject to line interference but far more flexible. With this technique, timesharing service can be established or discontinued at any point where the user has a tele- phone instrument. Timesharing transmissions can be carried over many different kinds of communication lines. In general, line costs are directly related to the transmission capacity and length of a given line . The least expensive, lowest-capacity transmission line is known as a half-duplex circuit. This is simply a circuit with two wires - one signal line and a return, or ground - between two points. With a half-duplex or two-wire circuit, data can be transmitted in only one direction at a time. Thus a terminal cannot be receiving data from the computer while the operator is sending data. This type of communication link has been used primarily for telegraphic service. The next step up is to use a four-wire, or full-duplex, circuit . This is the tyoe of connection normally established for telephone 137 conversions . Most timesharing services today use full -duplex circuits. These can be acquired either through dial service or on a leased-li.ne basis. (With leasad-lina service, a full-duplex ine is rented on a~ regular basis from telephone common carriers.) In general , a full- duplex line has the capacity to transmit or receive at a rate of up to 2400 baud, or bits of data oer second. This is equivalent to approximately 2^0 characters per second . Consideration of this line capacity gives further dimension to earlier discussions of terminal speed and automated transmission from off-line storage media. Recorded data can be transmitted at speeds of up to 240 characters per second. However, even under automatic operation, printing terminals are limited to 30 characters oer second- and a typist entering data directly from a keyboard is effectively limited to seven or eiaht characters per second . Where data transmission requirements are greater, additional lines can be added. In general , communication lines with capacities greater than full -duplex are known as broadband service . Transmission capa- b ili ties are directly proportional to the lines available. Thus four lines would make a transmission rata of 4800 baud available, eight lines would carry 9600 baud, and so on. Services regularly available from telephone carriers extend to 32 lines. However, users of time- sharing utility services will rarely require or encounter services involving more than full-duplex lines. In some cases, however, timesharing utilities do use a technique known as multiplexing to concentrate transmission from a number of users over the same telephone lines. Multiplexors are satellite communication processors. (Minicomputers are often used for multi- plexing.) A large number of timesharing users, sometimes as many as 132, can be linked to a single multiplexing point. ..Their trans- missions are then carried from the multiplexor to the central computer over either full-duplex or broadband lines. Typically, a multiplexor will be set up in a city remote from the central computer . For example, many timesharing companies operate computers in New York. These organizations then establish multiplexing points in major cities such as Chicago and Los Angeles, where users can link into the national timesharing network through local telephone calls. •U.S. GOVERNMENT PRINTING OFFICE : 19800-328-231/6531 138 N CO 0) s; O j/i ct c n <-t (/ * — 1 1 CD IT X CD O D a a CD c N c -> (J FEDERALLY COORDINATED PROGRAM (FCP) OF HIGHWAY RESEARCH AND DEVELOPMENT The Offices of Research and Development (R&D) of the Federal Highway Administration (FHWA) are responsible for a broad program of staff and contract research and development and a Federal-aid program, conducted by or through the State highway transportation agencies, that includes the Highway Planning and Research (HP&R) program and the National Cooperative Highway Research Program (NCHRP) managed by the Transportation Research Board. The FCP is a carefully selected group of proj- ects that uses research and development resources to obtain timely solutions to urgent national highway engineering problems.* The diagonal double stripe on the cover of this report represents a highway and is color-coded to identify the FCP category that the report falls under. A red stripe is used for category 1, dark blue for category 2, light blue for category 3, brown for category 4, gray for category 5, green for categories 6 and 7, and an orange stripe identifies category 0. FCP Category Descriptions 1. Improved Highway Design and Operation for Safety Safety R&D addresses problems associated with the responsibilities of the FHWA under the Highway Safety Act and includes investigation of appropriate design standards, roadside hardware, signing, and physical and scientific data for the formulation of improved safety regulations. 2. Reduction of Traffic Congestion, and Improved Operational Efficiency Traffic R&D is concerned with increasing the operational efficiency of existing highways by advancing technology, by improving designs for existing as well as new facilities, and by balancing the demand-capacity relationship through traffic management techniques such as bus and carpool preferential treatment, motorist information, and rerouting of traffic. 3. Environmental Considerations in Highway Design, Location, Construction, and Opera- tion Environmental R&D is directed toward identify- ing and evaluating highway elements that affect * The complete seven-volume official statement of the FCP is available from the National Technical Information Service, Springfield, Va. 22161. Single copies of the introductory volume are available without charge from Program Analysis (HRD-3), Offices of Research and Development, Federal Highway Administration, Washington, D.C. 20590. the quality of the human environment. The goals are reduction of adverse highway and traffic impacts, and protection and enhancement of the environment. 4. Improved Materials Utilization and Durability Materials R&D is concerned with expanding the knowledge and technology of materials properties, using available natural materials, improving struc- tural foundation materials, recycling highway materials, converting industrial wastes into useful highway products, developing extender or substitute materials for those in short supply, and developing more rapid and reliable testing procedures. The goals are lower highway con- struction costs and extended maintenance-free operation. 5. Improved Design to Reduce Costs, Extend Life Expectancy, and Insure Structural Safety Structural R&D is concerned with furthering the latest technological advances in structural and hydraulic designs, fabrication processes, and construction techniques to provide safe, efficient highways at reasonable costs. 6. Improved Technology for Highway Construction This category is concerned with the research, development, and implementation of highway construction technology to increase productivity, reduce energy consumption, conserve dwindling resources, and reduce costs while improving the quality and methods of construction. 7. Improved Technology for Highway Maintenance This category addresses problems in preserving the Nation's highways and includes activities in physical maintenance, traffic services, manage- ment, and equipment. The goal is to maximize operational efficiency and safety to the traveling public while conserving resources. 0. Other New Studies This category, not included in the seven-volume official statement of the FCP, is concerned with HP&R and NCHRP studies not specifically related to FCP projects. These studies involve R&D support of other FHWA program office research. 0005b7fl0